We provide conic sections practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on conic sections skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of conic sections Questions

Question No | Questions | Class |
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1 | 34. Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x , which intersect the axis of the parabola at A and B, respectively. IfC is the centre of the circle through the points P, A and B and ZCPB = 0, then a value of tan o is: [JEE M 2018] (a) 2 (b) 3 (c) (d) = | 11 |

2 | The graph of the equation ( 4 y^{2}+x^{2}= ) 25 is A . a circle B. an ellipse c. a hyperbola D. a parabola E . a straight line | 11 |

3 | The eccentricity of the hyperbola ( x y=4 ) is ( A cdot 2 ) B. ( sqrt{2} ) ( c cdot frac{3}{2} ) D. ( sqrt{3} ) | 11 |

4 | Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( frac{x^{2}}{49}+frac{y^{2}}{36}=1 ) | 11 |

5 | The foci of the ellipse ( frac{x^{2}}{16}+frac{y^{2}}{b^{2}}=1 ) and the hyperbola ( frac{x^{2}}{144}-frac{y^{2}}{81}=frac{1}{25} ) coincide Then, the value of ( b^{2} ) is : A . 5 B. 7 c. 9 D. | 11 |

6 | Which of the following equations represents parametrically, parabolic profile? ( mathbf{A} cdot x=3 cos t ; y=4 sin t ) B ( x^{2}-2=-cos t ; y=4 cos ^{2} frac{t}{2} ) ( mathbf{c} cdot sqrt{x}=tan t ; sqrt{y}=sec t ) D. ( x=sqrt{1-sin t} ; y=sin frac{t}{2}+cos frac{t}{2} ) | 11 |

7 | Length of the latusrectum of the hyperbola ( boldsymbol{x} boldsymbol{y}=boldsymbol{c}, ) is equal to A ( .2 c ) B. ( sqrt{2} c ) c. ( 2 sqrt{2} c ) D. ( 4 c ) | 11 |

8 | Find the value of ( p ) when the parabola ( y^{2}=4 p x ) goes through the point ( (i)(3,- ) 2) and (ii) (9,-12) | 11 |

9 | The equation of the circle passing through (3,6) and whose centre is (2,-1) is A ( cdot x^{2}+y^{2}-4 x+2 y=45 ) B . ( x^{2}+y^{2}-2 y+45=0 ) c. ( x^{2}+y^{2}+4 x-2 y=45 ) D. ( x^{2}+y^{2}+2 y+45=0 ) | 11 |

10 | ( P ) is a point on the ellipse having (3,4) and (3,-2) as the ends of minor axis. If the sum of the focal distances of ( boldsymbol{P} ) be equal to 10 then its equation is A ( cdot frac{(x-3)^{2}}{36}+frac{(y-1)^{2}}{12}=1 ) в. ( frac{(x-3)^{2}}{36}+frac{(y-1)^{2}}{25}=1 ) c. ( frac{(x-3)^{2}}{25}+frac{(y-1)^{2}}{9}=1 ) D. ( frac{(x-3)^{2}}{16}+frac{(y-1)^{2}}{7}=1 ) | 11 |

11 | The equation of the circle passing through the point (-1,2) and having two diameters along the pair of lines ( x^{2}-y^{2}-4 x+2 y+3=0 ) is A ( cdot x^{2}+y^{2}-4 x-2 y+5=0 ) B ( cdot x^{2}+y^{2}+4 x+2 y-5=0 ) c. ( x^{2}+y^{2}-4 x-2 y-5=0 ) D. ( x^{2}+y^{2}+4 x+2 y+5=0 ) | 11 |

12 | Find the equation of parabola with vertex (0,0)( & ) focus at (0,2) | 11 |

13 | For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum. ( boldsymbol{x}^{2}=-mathbf{9} boldsymbol{y} ) | 11 |

14 | The eccentricity of the conic ( x^{2}+ ) ( 2 y^{2}-2 x+3 y+2=0 ) is ( mathbf{A} cdot mathbf{0} ) B. ( frac{1}{sqrt{2}} ) ( c cdot frac{1}{2} ) D. ( sqrt{2} ) ( E ) | 11 |

15 | ( S_{1}, S_{2} ) are foci of an ellipse of major axis of length 10 units and ( P ) is any point on the ellipse such that perimeter of triangle ( P S_{1} S_{2} ) is ( 15 . ) Then eccentricity of the ellipse is: A . 0.5 B. 0.25 c. 0.28 D. 0.75 | 11 |

16 | Find the length of the latus rectum, the eccentricity and the coordinates of the foci of the ellipse ( x^{2}+3 y^{2}=a^{2} ) | 11 |

17 | Let ( S ) and ( S^{prime} ) be two foci of the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 . ) If a circle described on ( S S^{prime} ) as diameter intersects the ellipse in real and distinct points, then the eccentricity ( e ) of the ellipse satisfies ( ^{A} cdot e=frac{1}{sqrt{2}} ) в. ( _{e} inleft(frac{1}{sqrt{2}}, 1right) ) ( ^{mathrm{c}} cdot_{e} inleft(0, frac{1}{sqrt{2}}right) ) D. None of these | 11 |

18 | The centre of the ellipse ( 4 x^{2}+y^{2}- ) ( 8 x+4 y-8=0 ) is A ( .(0,2) ) в. (2,-1) c. (2,1) () D. (1,2) | 11 |

19 | In an ellipse, the distance between its focii is 6 and minor axis is ( 8 . ) Then its’ eccentricity is A ( cdot frac{3}{5} ) B. ( frac{1}{2} ) ( c cdot frac{4}{5} ) D. ( frac{1}{sqrt{5}} ) | 11 |

20 | A series of concentric ellipses ( epsilon_{1}, epsilon_{2}, epsilon_{3}, cdots in_{n} ) are drawn such that ( epsilon_{n} ) touches the extremities of the major axis of ( epsilon_{n-1} ) and the focii of ( epsilon_{n} ) coincides with the extremities of the minor axis of ( epsilon_{n-1} ) if the ( e ) of the ellipse is independent on ( n, ) then the value of ( e ? ) | 11 |

21 | For the ellipse ( 12 x^{2}+4 y^{2}+24 x- ) ( mathbf{1 6} boldsymbol{y}+mathbf{2 5}=mathbf{0} ) A. centre is (-1,2) B. Length of axes are ( sqrt{3} a n d 1 ) ( ^{mathrm{c}} cdot_{text {eceentricity is }} sqrt{frac{2}{3}} ) D. All of these | 11 |

22 | The equation ( 3 x^{2}-2 x y+y^{2}=0 ) represents: A . a circle B. hyperbola c. a pair of lines D. none of these | 11 |

23 | A thin rod of length ( l ) in the shape of a semicircle is pivoted at one of its ends such that it is free to oscillate in its own plane. The frequency ( boldsymbol{f} ) of small oscillations of the semicircular rod is : A ( cdot frac{1}{2 pi} sqrt{frac{g pi}{2 l}} ) в. ( frac{1}{2 pi} sqrt{frac{g sqrt{pi^{2}+4}}{2 l}} ) c. ( frac{1}{2 pi} sqrt{frac{g sqrt{pi+2}}{l}} ) D. ( frac{1}{2 pi} sqrt{frac{g sqrt{pi^{2}+1}}{2 pi l}} ) | 11 |

24 | A circle is described with minor axis of the ellipse as diameter. If the foci lie on the circle, then the eccentricty of the ellipse is A ( cdot frac{1}{sqrt{3}} ) в. ( frac{1}{sqrt{2}} ) ( c cdot frac{1}{2} ) D. ( frac{1}{sqrt{5}} ) | 11 |

25 | les 2x – 3y=5 and 3x – 4y=7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is (a) x2 + y2 + 2x – 2y=62 (1989 – 2 Marks) (b) x2 + y2 + 2x – 2y=47 (C) x2 + y2 – 2x +2y=47 (d) x2 + y2– 2x + 2y =62 | 11 |

26 | Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for ( y ) ( 2=10 x ) | 11 |

27 | The area of an ellipse is ( 8 pi ) sq. units. Its distance between the foci is ( 4 sqrt{3} ), then ( mathbf{e}= ) ( mathbf{A} cdot sin 30^{circ} ) B. ( sin 45^{circ} ) c. ( sin 60^{circ} ) ( mathbf{D} cdot sin 75^{circ} ) | 11 |

28 | An ellipse having foci at (3,1) and (1,1) passes through the point (1,3) Its eccentricity is: A ( cdot sqrt{2}-1 ) B. ( sqrt{3}-1 ) c. ( frac{1}{2}(sqrt{2}-1) ) D. ( frac{1}{2}(sqrt{3}-1) ) | 11 |

29 | 34. .X _Y_=1 is inscribed in a rectangle R The ellipse E1 : + 9xyz whose sides are parallel to the coordinate axes. Another ellipse E, passing through the point (0,4) circumscribes the rectangle R. The eccentricity of the ellipse E2 is (2012) | 11 |

30 | The centre of circle inscribed in square formed by scribed in square formed by the lines x2 – 8x + 12 =0 and y2 – 14y+45 = 0, is (20035) (a) (4,7) (b) (7,4) (c) (9,4) (d) (4,9) | 11 |

31 | Find the coordinates of the foci, the vertices the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( frac{x^{2}}{4}+frac{y^{2}}{25}=1 ) | 11 |

32 | Which of the following is/are not false? This question has multiple correct options A. The mid point of the line segment joining the foci is called the centre of the ellipse. B. The line segment through the foci of the ellipse is called the major axis. C. The end points of the major axis are called the vertices of the ellipse. D. Ellipse is symmetric with respect to Y-axis only. | 11 |

33 | For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum. ( boldsymbol{x}^{2}=mathbf{1 6} boldsymbol{y} ) | 11 |

34 | 27. The normal to the curve, x2 + 2xy – 3y2 = 0, at(1,1) (JEE M 2015] (a) meets the curve again in the third quadrant. (b) meets the curve again in the fourth quadrant. (c) does not meet the curve again. (d) meets the curve again in the second quadrant. | 11 |

35 | I. : Find the equation of the circle whose radius is 5 and which touches the circle x2 + y2 – 2x – 4y-20=0 at the point (5,5). (1978) | 11 |

36 | If ( t ) is a parameter,then ( boldsymbol{x}=boldsymbol{a}left(boldsymbol{t}+frac{mathbf{1}}{boldsymbol{t}}right) ) and ( y=bleft(t-frac{1}{t}right) ) represent A. An ellipse B. A circle c. A pair of straight lines D. A hyperbola | 11 |

37 | 33. Tangents are drawn to the hyperbola 4×2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of APTQ is : [JEEM 2018] (a) 5413 (b) 6013 (©) 3615 (d) 4515 | 11 |

38 | Latus rectum of a parabola is a ( ldots ldots . . ) line segment with respect to the axis of the parabola through the focus whose endpoints lie on the parabola. A. perpendicular B. parallel c. tilted D. None of these | 11 |

39 | Find equation of latus rectum of the parabola ( (x+1)^{2}=32 y ) A ( . y=32 ) B . ( x-8=0 ) ( mathbf{c} cdot y-8=0 ) D. ( x=32 ) | 11 |

40 | -Topic-wal D 14. Let P and Q be distinct points Let P and Q be distinct points on the parabola y = 2x such nat a circle with PO as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle AOPQ is 3 | 11 |

41 | Find the eccentricity of an ellipse, if its latus rectum be equal to one half its minor axis. | 11 |

42 | Find the equation of the ellipse in the standard form whose distance between foci is 2 and the length of latus rectum is ( frac{15}{2} ) | 11 |

43 | 25. be the circle with centre at (1, 1) and radius = 1. If Tis the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to [JEE M 2014] (a) | 11 |

44 | Find the locus of a point which moves in such a way that the sum of its distances from(4,3) and (4,1) is 5. | 11 |

45 | An ellipse passing through the point ( (2 sqrt{13}, 4) ) has its foci at (-4,1) and ( (4,1), ) then its eccentricity is A ( cdot frac{2}{3} ) B. ( frac{1}{3} ) ( c cdot frac{1}{4} ) D. | 11 |

46 | T U VUIUUS UIP 21. The circle x2 + y2 = 4x+8y+5 intersects the line 3x – 4y=m at two distinct points if [2010] (a) – 35<m<15 (b) 15<m<65 (c) 35<m<85 (d) -85<m<-35 2 2 2 O | 11 |

47 | Find the co-ordinates of the point from which tangents drawn to the circle ( x^{2}+y^{2}-6 x-8 y+3=0 ) such that the mid point of its chord of contact is (1,1) | 11 |

48 | Find the equation of centre (1,1) and radius ( sqrt{2} ) | 11 |

49 | Find the equation of the following curve in cartesian form ( boldsymbol{x}=-mathbf{1}+mathbf{2} sin boldsymbol{theta}, boldsymbol{y}= ) ( 1+2 cos theta . ) find the centre and radius of circle. | 11 |

50 | 15. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is Then the length of the semi-major axis is [2008] | 11 |

51 | The latus rectum of the hyperbola ( 16 x^{2}-9 y^{2}=144 ) is A ( cdot frac{13}{6} ) в. ( frac{32}{3} ) ( c cdot frac{8}{3} ) D. ( frac{4}{3} ) | 11 |

52 | 32. Let P(6,3) be a point on the hyperbola 5 =1. If the al normal at the point P intersects the x-axis at (9,0), then the eccentricity of the hyperbola is (2011) (c) 2 (d) 3 | 11 |

53 | 17. Normals are drawn Normals are drawn from the point P with slopes m 1, m,m, to the parabola y2 = 4x. If locus of P with m, m2 = a is a part of the parabola itself then find a. (2003 – 4 Marks) 4 ot : | 11 |

54 | A variable point ( boldsymbol{P} ) on the ellipse of eccentricity is joined to the foci ( S ) and ( s^{prime} . ) The eccentricity of the locus of the in cetre of the triangle ( P S S^{1} ) is A ( cdot sqrt{frac{2 e}{1+e}} ) B. ( sqrt{frac{e}{1+e}} ) c. ( sqrt{frac{1-e}{1+e}} ) D. ( frac{e}{2(1+e)} ) | 11 |

55 | For the parabola ( boldsymbol{y}^{2}+mathbf{8} boldsymbol{x}-mathbf{1 2} boldsymbol{y}+mathbf{2 0}= ) ( mathbf{0} ) This question has multiple correct options A. vertex is (2,6) B. Focus is (0.6) c. Latusrectum 4 D. Axis ( y=6 ) | 11 |

56 | For an ellipse, ( A ) and ( B ) are the ends of major axis and minor axis respectively. Area of ( Delta O A B ) is 16 sq.units and ( e= ) ( frac{sqrt{3}}{2}, ) then equation of the ellipse is: ( stackrel{text { A }}{-} frac{x^{2}}{32}+frac{y^{2}}{8}=1 ) в. ( frac{x^{2}}{16}+frac{y^{2}}{64}=1 ) c. ( frac{x^{2}}{64}+frac{y^{2}}{8}=1 ) D. ( frac{x^{2}}{64}+frac{y^{2}}{16}=1 ) | 11 |

57 | Find the equation of the hyperbola whose foci are ( (0, pm sqrt{10}) ) and passing through the point (2,3) | 11 |

58 | ( S ) and ( T ) are the foci of an ellipse and ( B ) is an end of the minor axis. If ( S T B ) is an equilateral triangle, then what is the value of ( e ) ? A ( cdot frac{1}{4} ) B. ( frac{1}{3} ) ( c cdot frac{1}{2} ) D. ( frac{2}{3} ) | 11 |

59 | The lines ( 2 x-3 y=5 ) and ( 3 x-4 y=7 ) intersect at the center of the circle whose area is 154 sq. units, then equation of circle is A ( cdot x^{2}+y^{2}-2 x+2 y=47 ) B. ( x^{2}+y^{2}+2 x-2 y=31 ) c. ( x^{2}+y^{2}-2 x-2 y=47 ) D. ( x^{2}+y^{2}-2 x-2 y=31 ) | 11 |

60 | 8. Let L, be a strainght line passing through the origin and L, be the straight line x +y = 1. If the intercepts made by the circle x2 + y2 – x+3y = 0 on L, and L, are equal, then which of the following equations can represent L,? (1999 – 3 Marks (a) x+y=0 (b) x-y=0 (c) x+7y=0 (d) x-7y = 0 | 11 |

61 | Which of the following is/are correct? This question has multiple correct options A. Parabola is symmetric with respect to the axis of the parabola. B. Length of latus rectum of a parabola, ( y^{2}=4 a x ) is ( 4 a ) C. A line through the focus and perpendicular to the directrix is called the axis of the parabola. D. The point of intersection of a parabola with the axis is called the vertex of the parabola. | 11 |

62 | 14. If the pair of lines ax2 +2 (a + b)xy + by of lines ar? +2 (a + b)xy + by2 = 0 lie along imeters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the a another sector then [2005] (a) 3a2 – 10ab + 362 = 0 (b) 3a2 – 2ab + 362 = 0 (©) 3a+10ab + 362 = 0 (d) 3a? + 2ab + 362 = 0 | 11 |

63 | 2 le passes through the point (a, b) and cuts the circle 2 + y2 = 4 orthogonally, then the locus of its centre is (a) 2ax – 2by – (a² +6²+4)= 0 [2004] (b) 2ax + 2by – (a? +b+ 4) = 0 (C) 2ax – 2by +(a? + b2 + 4) = 0 (d) 2ax + 2by + (a? +62 + 4) = 0 | 11 |

64 | In an ellipse the length of minor axis is equal to the distance between the foci, the length of latus rectum is 10 and ( e=frac{1}{sqrt{2}} . ) Then the length of semi major axis is: A . 16 B . 18 c. 10 D. 22 | 11 |

65 | A point ( (alpha, beta) ) lies on a circle ( x^{2}+y^{2}= ) 1, then locus of the point ( (3 alpha+2 beta) ) is a / an. A. Straight line B. Ellipse c. Parabola D. None of these | 11 |

66 | Find the equations of the circle passing through (4,3) and touching the lines x + y = 2 and x-y=2. (1982-3 Marks) | 11 |

67 | Find the direction cosines of the unit vector perpendicular to the plane ( vec{r} cdot(6 hat{i}-3 hat{j}-2 k)+1=0 ) passing through the origin. | 11 |

68 | Find the equation of the hyperbola whose Transverse and Conjugate axes are the ( x ) and ( y ) axes respectively, given that the length of conjugate axis is 5 and distance between the foci is 13 | 11 |

69 | 26. Let O be the vertex and Q be any point on the parabola, x = 8y. If the point P divides the line segment OQ internally in the ratio 1:3, then locus of P is: [JEE M 2015] (a) y2 = 2x (b) x2 = 2y (c) x2 =y (d) y2 = X | 11 |

70 | The total number of real tangents that can be drawn to the ellipse ( 3 x^{2}+ ) ( 5 y^{2}=32 ) and ( 25 x^{2}+9 y^{2}=450 ) passing through (3,5) is ( A cdot 0 ) B . 2 ( c .3 ) D. | 11 |

71 | 19. ition of the family of circles with fixed The differential equation of the family of circie radius 5 units and centre on the line y=2 is (a) (x – 2)y2 = 25+(y-2)2 (b) (y-2)y’2 = 25-(y-2)2 (c) (-2)?y2 = 25-(y-2)2 (d) (x – 2)2 y2 = 25 -(y-2)2 | 11 |

72 | 5. A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014) (a) radius of S is 8 (b) radius of Sis 7. (c) centre of Sis (-7, 1) (d) centre of S is (-8,1) | 11 |

73 | The centre, vertex, focus of a conic are ( (0,0),(0,5),(0,6) . ) Its length of latus rectum is A ( cdot frac{11}{5} ) в. ( frac{7}{5} ) c. ( frac{14}{5} ) D. ( frac{22}{5} ) | 11 |

74 | The centre of a circle passing through the points (0,0), (1, and touching the circle x2 + y2 =9 is (1992 – 2 Marks) | 11 |

75 | Prove that the sum of the distances from the focus of the points in which a conic is intersected by any circle, whose centre is at a fixed point on the transverse axis, is constant. | 11 |

76 | Through a fixed point (h, k) secants are drawn to the circle x2 + y2 = r2. Show that the locus of the mid-points of the secants intercepted by the circle is x2 + y2 = hx + ky. (1983 – 5 Marks) | 11 |

77 | The eccentricity of the conic ( 9 x^{2}+ ) ( 5 y^{2}-54 x-40 y+116=0 ) is: A ( -frac{1}{3} ) B. ( frac{2}{3} ) ( c cdot frac{4}{9} ) D. ( frac{2}{sqrt{5}} ) | 11 |

78 | The locus of the centre of a circle, which touches externany the circle x2 + y2 – 6x – 6y + 14 = 0 and also touch is, is given by the equation: (1993 – 1 Marks) (a) x2 – 6x – 10y + 14 =0 (b) x2 – 10x -6y + 14 = 0 (C) y2 – 6x – 10y + 14 =0 (d) y2 – 10x – 6y + 14 = 0 2. et | 11 |

79 | The point at which the hyperbola intersects the transverse axis are called the ( ldots ). of the hyperbola. | 11 |

80 | Find the eccentricity of that ellipse, whose latus rectum is half of the minor axis. | 11 |

81 | Find the coordinates of the point at which the circles x + y – 4x – 2y= 4 and x2 + y2 – 12x – 8y=-36 touch each other. Also find equations common tangents touching the circles in the distinct points. (1993 – 5 Marks) | 11 |

82 | The ends of the latus rectum of the parabola ( boldsymbol{x}^{2}+mathbf{1 0 x}-mathbf{1 6 y}+mathbf{2 5}=mathbf{0} ) are A ( cdot(3,4),(-13,4) ) B. (5,-8),(-5,8) c. (3,-4),(13,4) D. (-3,4),(13,-4) | 11 |

83 | 8. The circle x2 + y2 – 4x-4y+4=0 is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is x + y – xy + k(x2 + y2)1/2 = 0. Find k. (1987- 4 Marks) | 11 |

84 | 17. The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse – 5 (a) 27/4 sq. units (c) 27/2 sq. units (b) 9 sq. units (d) 27 sq. units (2003) | 11 |

85 | 2. IfP=(x, y), F, =(3,0), F, =(-3,0) and 16×2 + 25y2 = 400, then PF, +PF, equals (1998 – 2 Marks) (a) 8 (6) 6 (c) 10 (d) 12 | 11 |

86 | The equation ( 16 x^{2}-3 y^{2}-32 x+ ) ( 12 y-44=0 ) represents a hyperbola. A. The length of whose transverse axis is ( 4 sqrt{3} ) B. The length of whose conjugate axis is 4 c. whose centre is (-1,2) D. whose eccentricity is ( sqrt{frac{19}{3}} ) | 11 |

87 | 12. Find the co-ordinates of all the points P on the ellipse r2 y2 5 =1, for which the area of the triangle PON is maximum, where O denotes the origin and N, the foot of the perpendicular from O to the tangent at P. (1999 – 10 Marks) | 11 |

88 | Let ( A B C D ) be a square of side length 1 and ( Gamma ) a circle passing through ( B ) and ( C ) and touching ( A D . ) The radius of ( Gamma ) is A в. c. ( frac{1}{sqrt{2}} ) D. | 11 |

89 | The eccentricity of the ellipse ( 25 x^{2}+ ) ( 16^{2}=400 ) is A ( cdot frac{3}{5} ) B. ( frac{1}{3} ) ( c cdot frac{2}{5} ) D. | 11 |

90 | Suppose that the normals drawn at three different points on the parabola y2 = 4x pass through the point (h, k). Show that h>2. (1981 – 4 Marks) | 11 |

91 | 2. The normal at the point (bt,2,2bt,) on a parabola meets the parabola again in the point (bt22, 2btą), then (b) t2 =4-2 [2003] 11 (d) 12=1- | 11 |

92 | The locus of a point P(a, b) moving under the condition that the line y = ax +ß is a tangent to the hyperbola x2 12 [2005] a² 62 (a) an ellipse c) a parabola (b) a circle (d) a hyperbola 11. | 11 |

93 | lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a having area as 154 sq.units. Then the equation of the [2003] (a) x2 + y2 – 2x +2y = 62 (b) x2 + y2 + 2x – 2y = 62. (C) x2 + y2 + 2x – 2y = 47. (d) x2 + y2 – 2x + 2y = 47 circle is 11 | 11 |

94 | The equation of the latusrecta of the ellipse ( 9 x^{2}+4^{2}-18 x-8 y-23=0 ) are A ( . y=pm sqrt{5} ) В. ( x=pm sqrt{5} ) c. ( y=1 pm sqrt{5} ) D. ( x=1 pm sqrt{5} ) | 11 |

95 | If the eccentricities of the hyperbola ( frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1 ) and ( frac{y^{2}}{b^{2}}-frac{x^{2}}{a^{2}}=1 ) be ( e ) and ( e_{1}, ) then ( frac{1}{e^{2}}+frac{1}{e_{1}^{2}}= ) ( mathbf{A} cdot mathbf{1} ) B. 2 ( c cdot 3 ) D. None of these | 11 |

96 | Find the equation of the ellipse whose vertices are ( (pm mathbf{3}, mathbf{0}) ) and foci are (±2,0) | 11 |

97 | 31. A hyperbola passes through the point P(V2,V3) and has foci at (+2,0). Then the tangent to this hyperbola at P also passes through the point : [JEEM 2017] (a) (-12,-v3 (b) (312,213) (0) (2/2, 3/3) (2) (13, 12) | 11 |

98 | The equation of the image of the circle ( x^{2}+y^{2}+16 x-24 y+183=0 ) by the line mirror ( 4 x+7 y+13=0 ) is: A ( cdot x^{2}+y^{2}+32 x-4 y+235=0 ) B. ( x^{2}+y^{2}+32 x+4 y-235=0 ) C. ( x^{2}+y^{2}+32 x-4 y-235=0 ) D. ( x^{2}+y^{2}+32 x+4 y+235=0 ) | 11 |

99 | If the line ( y=x sqrt{3}-3 ) cuts the parabola ( boldsymbol{y}^{2}=boldsymbol{x}+boldsymbol{2} ) at ( boldsymbol{P} ) and ( boldsymbol{Q} ) and if ( A ) be the points ( (sqrt{3}, 0), ) then ( A P . A Q ) is A ( cdot frac{2}{3}(sqrt{3}+2) ) B. ( frac{4}{3}(sqrt{3}+2) ) c. ( frac{4}{3}(2-sqrt{3}) ) D. ( frac{4}{6-3 sqrt{3}} ) | 11 |

100 | 6. Lines 5x+12y-10=0 and 5x – 12y-40 = 0 touch a circle C of diameter 6. If the centre of C, lies in the first quadrant, find the equation of the circle C, which is concentric with C, and cuts intercepts of length 8 on these lines. | 11 |

101 | Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola ( 9 y^{2}- ) ( 4 x^{2}=36 ) | 11 |

102 | 14. The triangle PQR is inscribed in the circle x2 + y2 = 25. If o and R have co-ordinates (3,4) and (4,3) respectively, then ZQPR is equal to (2000) | 11 |

103 | TOPIL 21. The angle between the tangents drav s drawn from the point (1.4) to the parabola y2 = 4x is (a) TUG (6) N4 (c) T3 (d) T2 (2004) | 11 |

104 | The focus of a conic is the origin and its corresponding directrix is ( 7 x-y- ) ( mathbf{1 0}=mathbf{0 .} ) If length of its latus rectum is 2 then its eccentricity is: A ( cdot sqrt{2} ) B. 1 c. ( frac{1}{sqrt{2}} ) D. ( frac{1}{2} ) | 11 |

105 | – – – 10. The angle between a pair of tangents drawn from a point P to the parabola y2 =4ax is 45°. Show that the locus of the point P is a hyperbola. (1998 – 8 Marks) | 11 |

106 | A straight line through the vertex P of a triangle POR intersects the side OR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then (2008) 2 11 (a) ps sīTOS XSR (6) PS ST TOS XSR 1 1,4 1 1 4 © PS + STOR (d) PS+ STOR | 11 |

107 | Given below are Matching type questions, with two columns(each having some items) each.Each item of column ( I ) has to be matched with the items of column ( I I ), by enclosing the correct match. Note:An item of column ( I ) can be matched with more than one items of columnII.All the items of column ( I I ) have to be matched. The equation of conics represented by the general equation of second degree ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2 h x} boldsymbol{y}+boldsymbol{b} boldsymbol{y}^{2}+boldsymbol{2} boldsymbol{g} boldsymbol{x}+boldsymbol{2} boldsymbol{f} boldsymbol{y}+boldsymbol{c}= ) 0 and the discriminant of above equation is represented by ( triangle, ) where ( triangle=a b c+ ) ( 2 f g h-a f^{2}-b g^{2}-c h^{2} ) or ( left(begin{array}{lll}a & h & g \ h & b & f \ g & f & cend{array}right) ) Now, match the entries from the following two columns | 11 |

108 | The equation ( frac{x^{2}}{8-t}+frac{y^{2}}{t-4}=1 ) will represent an ellipse if A. ( t in(1,5) ) B. ( t in(2,8) ) c. ( t in(4,8)-{6} ) D. ( t in(4,10)-{6} ) | 11 |

109 | 13. Ifa circle passes through the point (a, b) and cuts the circle x2 + y2 = p< orthogonally, then the equation of the locus of its centre is [2005] (a) x2 + y2 – 3ax – 4by +(a? +62 – p2)=0 (b) 2ax +2by-(a? – b? +p?)=0 (C) x² + y2 – 2ax – 3by +(a? – b2 – p2)=0 (d) 2ax +2by-(a? +62 +p)=0 | 11 |

110 | The equation of the ellipse whose equation of directrix is ( 3 x+4 y-5=0 ) coordinates of the focus are (1,2) and the eccentricity is ( frac{1}{2} ) is ( 91 x^{2}+84 y^{2}- ) ( 24 x y-170 x-360 y+475=0 ) A. True B. False | 11 |

111 | An ellipse with centre at (0,0) cuts ( x ) axis at (3,0) and ( (-3,0) . ) If its ( e=frac{1}{2} ) then the length of the semiminor axis is: A ( .2 sqrt{3} ) B. ( sqrt{5} ) c. ( 3 sqrt{2} ) D. ( frac{3 sqrt{3}}{2} ) | 11 |

112 | Find the latus rectum, the eccentricity, and the coordinates of the foci, of the ellipses (1) ( x^{2}+3 y^{2}=a^{2}, ) (2) ( 5 x^{2}+4 y^{2}=1 ) and (3) ( 9 x^{2}+5 y^{2}-30 y=0 ) | 11 |

113 | The tangent at any point ( P(a cos theta, b sin theta) ) on the ellipse ( frac{x^{2}}{a^{2}}+ ) ( frac{boldsymbol{y}^{2}}{boldsymbol{b}^{2}}=1 ) meets the auxiliary circle at two point which subtend a right angle at the centre, then eccentricity is A ( cdot frac{1}{sqrt{1+sin ^{2} theta}} ) в. ( frac{1}{sqrt{2-cos ^{2} theta}} ) c. ( frac{1}{sqrt{1+tan 2 theta}} ) D. noneofthese | 11 |

114 | 68. The radii of two circles are 5cm and 3cm, the distance between their centres is 24 cm. Then the length of the transverse common tangent is (1) 16 cm (2) 15.2 cm (3) 162 cm (4) 15 cm | 11 |

115 | 20. If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x +y=p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k? (JEE Adv. 2017) (a) p=-2, h=2, k=-4 (b) p=-1, h=1, k=-3 (c) p=2, h=3, k=-4 (d) p=5, h=4, k=-3 | 11 |

116 | If ( L_{1} L_{2} ) is the latusrectum of ( y^{2}=12 x ) ( P ) is any point on the directrix then the ( operatorname{area~of} Delta P L_{1} L_{2}= ) ( A cdot 32 ) B . 18 ( c .36 ) D. 16 | 11 |

117 | The length of the latus rectum of the parabola ( mathbf{1 6 9}left{(boldsymbol{x}-mathbf{1})^{2}+(boldsymbol{y}-mathbf{3})^{2}right}=(mathbf{5} boldsymbol{x}- ) ( 12 y+17)^{2} ) is A ( cdot frac{14}{11} ) в. ( frac{12}{13} ) c. ( frac{28}{13} ) D. none of these | 11 |

118 | If the the hyperbola ( frac{x^{2}}{4}-frac{y^{2}}{b^{2}}=1 ) passses though (4,3) ( mathbf{A} cdot b^{2}=3 ) B. ( b^{2}=9 ) ( mathbf{c} cdot b^{2}=4 ) D. ( b^{2}=100 ) | 11 |

119 | Find the equation to the circle : Whose radius is ( sqrt{a^{2}-b^{2}} ) and whose center is ( (-a,-b) ) | 11 |

120 | The length of latus rectum of ( frac{x^{2}}{9}+ ) ( frac{boldsymbol{y}^{2}}{2}=1 ) is ( A cdot frac{7}{4} ) B. ( frac{3}{4} ) ( c cdot frac{4}{3} ) D. None. | 11 |

121 | a) 1 (0) 14. If a > 26 > 0 then the positive value of m for which y = mx – 671+ m2 is a common tangent to x2 + y2 = 52 and (x – a)2 + y2 = 62 is (20025) 26 Va? – 462 (b) = 2b © 26 a-26 a-2b | 11 |

122 | ( S ) is one focus of an ellipse and ( P ) is any point on the ellipse. If the maximum and minimum values of ( S P ) are ( m ) and ( boldsymbol{n} ) respectively, then the length of semi major axis is A . AM of ( m, n ) в. G.M. of ( m, n ) с. нм от ( m, n ) D. AGP of ( m, n ) | 11 |

123 | The equation of the latus rectum of the hyperbola ( frac{(x-4)^{2}}{16}-frac{(y-3)^{2}}{20}=1 ) are? ( mathbf{A} cdot x=1 pm 5 ) B . ( x=4 pm 6 ) c. ( y=2 pm 6 ) D. ( y=3 pm 5 ) | 11 |

124 | The locus of the vertices of the family of parabolas [2006] | 11 |

125 | Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( frac{x^{2}}{36}+frac{y^{2}}{16}=1 ) | 11 |

126 | Find the equation of the circle whose diameters are along the lines ( 2 x- ) ( 3 y+12=0 ) and ( x+4 y-5=0 ) and whose area is 154 sq. units. | 11 |

127 | If (5,12) and (24,7) are the foci of an ellipse passing through the origin, then the eccentricity of the conic is A ( cdot frac{sqrt{386}}{12} ) B. ( frac{sqrt{386}}{13} ) c. ( frac{sqrt{386}}{25} ) D. ( frac{sqrt{386}}{38} ) | 11 |

128 | If latus rectum of an ellipse ( frac{x^{2}}{16}+ ) ( frac{boldsymbol{y}^{2}}{boldsymbol{b}^{2}}=1{0<boldsymbol{b}<4}, ) subtends angle ( mathbf{2} boldsymbol{theta} ) at farthest vertex such that ( operatorname{cosec} theta= ) ( sqrt{5} ) then which of the following options are correct: This question has multiple correct options A ( cdot e=frac{1}{2} ) B. no such ellipse exists c. ( b=2 sqrt{3} ) D. area of ( Delta ) formed by ( L R ) and nearest vertex is 6 sq units | 11 |

129 | 15. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix (2002) (a) x=-a (b) x=-a/2 (c) X=0 (d) x=a/2 | 11 |

130 | The AFC Curve passes through the Origin statement is – A. True B. False c. Partially True D. Nothing can be said | 11 |

131 | If the line x – 1 = 0 is the directrix of the parabola ye – kx + 8 = 0, then one of the values of k is ( (a) 1/8 (b) 8 (c) 4 (d) 1/4 1: the circle | 11 |

132 | For the points on the circle ( x^{2}+y^{2}- ) ( 2 x-2 y+1=0, ) the sum of maximum and minimum values of ( 4 x+3 y ) is A ( cdot frac{26}{3} ) B . 10 c. 12 D. 14 | 11 |

133 | Through a fixed point (h, k) secants are drawn to the circle x2 + y2 = r2. Show that the locus of the mid-points of the secants intercepted by the circle is x2 + y2 = hx + ky. (1983 – 5 Marks) | 11 |

134 | 5. (1994 – 4 MUTAS) Show that the locus of a point that divides a chord of slope 2 of the parabola y2 = 4x internally in the ratio 1: 2 is a parabola. Find the vertex of this parabola. (1995 – 5 Marks) of the | 11 |

135 | The length of the latus rectum of the parabola ( boldsymbol{x}=boldsymbol{a} boldsymbol{y}^{2}+boldsymbol{b} boldsymbol{y}+boldsymbol{c} ) is A ( cdot frac{a}{4} ) B. ( frac{a}{3} ) ( c cdot frac{1}{a} ) D. ( frac{1}{4 a} ) | 11 |

136 | Find the foci of the curve ( 16 x^{2}- ) ( mathbf{2 4 x y}+mathbf{9 y}^{2}+mathbf{2 8 x + 1 4 y}+mathbf{2 1}=mathbf{0} ) | 11 |

137 | The intercept on the line ( y=x ) by the ( operatorname{circle} x^{2}+y^{2}-2 x=0 ) is ( A B ) Equation of the circle with ( A B ) as a diameter is A ( cdot x^{2}+y^{2}+x+y=0 ) B . ( x^{2}+y^{2}-x-y=0 ) c. ( x^{2}+y^{2}+x-y=0 ) D. None of these | 11 |

138 | . 64 4 10. In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is [2006] (d) | 11 |

139 | 22. If the line 2x + V6 y=2 touches the hyperbola x2 – 2y =4, then the point of contact is (2004) (a) (-2, 0) (b) (-5,216) (d) (4,-16) | 11 |

140 | The locus of a planet orbiting around the sun is: A. A circle B. A straight line c. A semicircle D. An ellipse | 11 |

141 | 5. The axis of a parabola is along the line y=x and the distances of its vertex and focus from origin are 12 and 22 respectively. If vertex and focus both lie in the first quadrant. then the equation of the parabola is (2006 – 3M, -1) (a) (x + y)2 = (x -y-2) (b) (x – y)2 = (x + y-2) © (x – y)2 = 4 (x + y -2) (d) (x – y)2 = 8 (x + y-2) | 11 |

142 | [2004] If the lines 2x + 3y +1 = 0 and 3x – y -4 = 0 lie along diameter of a circle of circumference 10t, then the equation of the circle is (a) x² + y2 + 2x – 2y – 23 = 0 (b) x2 + y2 – 2x – 2y – 23 = 0 © x2 + y2 + 2x+2y – 23 = 0 (d) x² + y2 –2x+2y – 23 = 0 | 11 |

143 | The eccentricity of the conic represented by the equation ( x^{2}+ ) ( 2 y^{2}-2 x+3 y+2=0 ) is ( mathbf{A} cdot mathbf{0} ) B. ( frac{1}{2} ) c. ( frac{1}{sqrt{2}} ) D. ( sqrt{2} ) | 11 |

144 | 39. Equation of a common tangent to the circ x2 + y2 – 6x = 0 and the parabola, y2 = 4X, 18: [JEEM 2019-9 Jan (M) (a) 2 V3y=12x +1 (C) 2 V3 y=-x-12 (b) 13y=x+3 (d) 13 y=3x +1 | 11 |

145 | The graph represented by equations ( x=sin ^{2} t, y=2 cos t ) is A. hyperbola B. sine graph c. parabola D. straight line | 11 |

146 | Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( 4 x^{2}+9 y^{2}=36 ) | 11 |

147 | 38. Let 0 < 0 . If the eccentricity of the hyperbola r2 v2 cos?o sin’e 20 = 1 is greater than 2, then the length of its latus rectum lies in the interval: JEE M 2019-9 Jan (M) (a) (3,0) (b) (3/2,2] (C) (2,31 (d) (1,3/2] | 11 |

148 | The tangents at two points, ( P ) and ( Q ), of a conic meet in ( mathrm{T} ), and ( mathrm{S} ) is the focus prove that if the conic be a parabola, ( operatorname{then} S T^{2}=S P . S Q ) | 11 |

149 | Length of the latus rectum of the parabola ( 25left[(x-2)^{2}+(y-3)^{2}right]= ) ( (3 x-4 y+7)^{2} ) is : ( A cdot 4 ) B. 2 ( c cdot 1 / 5 ) D. 2/5 | 11 |

150 | If the length of the major axis of the ellipse ( left(frac{x^{2}}{a^{2}}right)+left(frac{y^{2}}{b^{2}}right)=1 ) is three times the length of minor axis, its eccentricity is: A ( cdot frac{1}{3} ) в. ( frac{1}{sqrt{3}} ) ( c cdot sqrt{frac{2}{3}} ) D. ( frac{2 sqrt{2}}{3} ) | 11 |

151 | Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( 36 x^{2}+4 y^{2}=144 ) | 11 |

152 | 6. Let P(x, y) and Q(x, y,), y, <0,y, <0, be the end points of the latus rectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latus rectum PQ are (2008) (a) x2 +213 y = 3+v3 (b) -213 y = 3+ 13 (C) x2 + 273 y = 3 -13 (d) x2 – 2/3 y = 3-13 | 11 |

153 | For ( boldsymbol{y}^{2}-mathbf{2 0 0} boldsymbol{x}=mathbf{0}, ) focal distance of a point ( (2,20), ) is A . 48 B. 50 c. 52 D. 20 | 11 |

154 | 8. If x=9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is (1999 – 2 Marks) (a) 9×2 – 8y2 + 18x –9=0 (b) 9×2 – 892 – 18x +9=0 (c) 9×2 – 8y2 – 18x –9=0 (d) 9×2 – 872 +18x+9=0 | 11 |

155 | State whether following statements are true or false Statement-1: The only circle having radius ( sqrt{10} ) and a diameter along line ( 2 x+y=5 ) is ( x^{2}+y^{2}-6 x+2 y=0 ) Statement-2: The line ( 2 x+y=5 ) is a normal to the circle ( x^{2}+y^{2}-6 x+ ) ( 2 y=0 ) A. Statement- 1 is false, statement- 2 is true. B. Statement-1 is true,statement-2 is true and statement 2 is NOT the correct explanation for statement-1. c. Statement-1 is true, statement-2 is false. D. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement- | 11 |

156 | Find the area of the partitions cut off by the hyperbola ( x^{2}-3 y^{2}=1 ) from the ellipse ( x^{2}+4 y^{2}=8 ) | 11 |

157 | If the equation ( 136left(x^{2}+y^{2}right)=(5 x+ ) ( 3 y+7)^{2} ) represents a conic, then its length of latus rectum is A ( cdot frac{7}{2 sqrt{34}} ) B. ( frac{7}{sqrt{34}} ) c. ( frac{14}{sqrt{34}} ) D. ( frac{9}{sqrt{34}} ) | 11 |

158 | ( S ) and ( T ) are the foci of an ellipse and ( B ) is an end of the minor axis, if ( triangle boldsymbol{S T B} ) is equilateral, then ( e ) is equals to: A ( cdot frac{1}{4} ) B. ( frac{1}{3} ) ( c cdot frac{1}{2} ) D. None of these | 11 |

159 | ( boldsymbol{E}_{1}=frac{boldsymbol{x}^{2}}{boldsymbol{a}^{2}}+frac{boldsymbol{y}^{2}}{boldsymbol{b}^{2}}-mathbf{1}=mathbf{0},(boldsymbol{a}>boldsymbol{b}) ) and ( boldsymbol{E}_{2}=frac{boldsymbol{x}^{2}}{boldsymbol{k}^{2}}+frac{boldsymbol{y}^{2}}{boldsymbol{b}^{2}}-mathbf{1}=mathbf{0},(boldsymbol{k}<boldsymbol{b}) boldsymbol{E}_{2} ) is inscribed in ( E_{1} . ) If ( E_{1} ) and ( E_{2} ) have same eccentricities then length of minor axis of ( boldsymbol{E}_{2}=boldsymbol{p}left(mathrm{LLR} text { of } boldsymbol{E}_{1}right) ) then ( boldsymbol{p}=? ) A ( cdot frac{1}{2} ) B. 1 ( c cdot frac{2}{3} ) D. | 11 |

160 | The asymptotes of a hyperbola having centre at the point (1,2) are parallel to the lines ( 3 x+4 y=0 ) and ( 4 x+5 y=0 ) If the hyperbola passes through the point ( (3,5), ) Find the equation of the hyperbola. | 11 |

161 | The equation of the circle which touches ( x ) -axis and whose center is (1,2) is ( mathbf{A} cdot x^{2}+y^{2}-2 x+4 y+1=0 ) B . ( x^{2}+y^{2}-2 x-4 y+1=0 ) ( mathbf{c} cdot x^{2}+y^{2}+2 x+4 y+1=0 ) D. ( x^{2}+y^{2}-4 x+2 y+4=0 ) | 11 |

162 | If the centre ( O ) of circle is the intersection of ( x- ) axis and line ( y= ) ( frac{4}{3} x+4, ) and the point (3,8) lies on circle, then the equation of circle will be A ( cdot x^{2}+y^{2}=25 ) B – ( (x+3)^{2}+y^{2}=25 ) c. ( (x+3)^{2}+y^{2}=100 ) D. ( (x+3)^{2}+(y-8)^{2}=100 ) | 11 |

163 | Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is 10 . | 11 |

164 | The eccentricity of the conic is ( frac{l}{r}= ) ( 2+3 cos theta+4 sin theta ) ( mathbf{A} cdot mathbf{3} ) B. 4 ( c .5 ) D. | 11 |

165 | 18. The point diametrically opposite to the point P(1,0) on the circle x2 + y2 + 2x + 4y -3=0 is [2008] (a) (3,-4) (b) (-3,4) (c) (-3,-4) (d) (3,4) | 11 |

166 | A hyperbola, having the transverse axis of length 2 sin , je confocal with the ellipse 3×2 + 4y2 = 12. Then its equation is (2007 – 3 marks) (a) x?cosec20-y-sec20 = 1 (b) x?sec20-y-cosec20 =1 (C) x-sin20- y2cos20=1 (d) x?cos20-yasin20=1 | 11 |

167 | The length of latus rectum of the hyperbola ( boldsymbol{x} boldsymbol{y}-mathbf{3} boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{7}=mathbf{0} ) is A .4 B. 3 ( c cdot 2 ) D. | 11 |

168 | 16. The equation of the common tangent to the curves yz = 8x and xy=-1 is (a) 3y=9x + 2 (b) y=2x + 1 (c) 2y=x+8 (d) y=x+2 (2002) | 11 |

169 | 20. Let 2×2 + y2 – 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA. (2001 – 5 Marks | 11 |

170 | 3. Consider the two curves Cy: y2 = 4x, C2: x2 + y2 – 6x +1=0. Then, (2008) 1 C, and C, touch each other only at one point. in C, and C, touch each other exactly at two points C, and C, intersect (but do not touch) at exactly two points (d). C, and C, neither intersect nor touch each other | 11 |

171 | A man running round a race course notes that the sum of the distance of two flag posts from him is always ( 10 m ) and the distance between the flag posts is 8 m. The area of the path he encloses in square metres is: A . ( 15 pi ) в. ( 20 pi ) c. ( 27 pi ) D. ( 30 pi ) | 11 |

172 | (1992- O MURS) Consider a family of circles passing through two fixed points A (3,7) and B(6,5). Show that the chords in which the circle x + y2 – 4x – 6y – 3 = 0 cuts the members of the family are concurrent at a point. Find the coordinate of this point. | 11 |

173 | Find the equation of the circle: Centered at (3,-2) with radius 4 ( mathbf{A} cdot x^{2}+y^{2}+6 x-4 y=3 ) B ( cdot x^{2}+y^{2}-6 x+4 y=3 ) C ( cdot x^{2}+y^{2}-3 x+2 y=-3 ) D. ( x^{2}+y^{2}+3 x-2 y=-3 ) | 11 |

174 | 21. Let C, and C, be two circles with C, lying inside C. A circle C lying inside C, touches C, internally and C, externally. Identify the locus of the centre of C. (2001 – 5 Marks) | 11 |

175 | If the latus rectum of an ellipse ( boldsymbol{x}^{2} tan ^{2} varphi+boldsymbol{y}^{2} sec ^{2} varphi=1 ) is ( 1 / 2, ) then ( varphi ) is ( mathbf{A} cdot pi / 2 ) в. ( pi / 6 ) c. ( pi / 3 ) D. ( 5 pi / 12 ) | 11 |

176 | 21. An ellipse is drawn by taking a diameter of the circle (x – 1) + y2 = 1 as its semi-minor axis and a diameter of the circle x2+(y-2)2=4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012] (a) 4×2 + y2 = 4 (b) x2 + 4y2=8 (c) 4×2 + y2 = 8 (d) x2 + 4y2 = 16 | 11 |

177 | Cantres of the three circles ( x^{2}+y^{2}-4 x-6 y-14=0 ) ( boldsymbol{x}^{2}+boldsymbol{y}^{2}+boldsymbol{2} boldsymbol{x}+boldsymbol{4} boldsymbol{y}-boldsymbol{5}=mathbf{0} ) and ( x^{2}+y^{2}-10 x-16 y+7=0 ) A. Are the vertices of a right triangle B. The vertices of an isosceles triangle which is not regular c. vertices of a regular triangle D. Are collinear | 11 |

178 | Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3,3) and directrix is ( 3 x-4 y=2 . ) Find also the length of the latus-rectum. | 11 |

179 | 2. Two circles x2 + y2 =6 and x2 + y2 – 6x +8=0 are given. Then the equation of the circle through their points of intersection and the point (1,1) is (1980) (a) x2 + y2 – 6x +4=0 (b) x2 + y2 – 3x + 1 = 0 (c) x2 + y2 – 4y +2=0 (d) none of these | 11 |

180 | UNTUV 1 14 0 (u 10 11. The circles x2 + y2 – 10x + 16 = 0 and x2 + y2 = pe in each other in two distinct points if (a) r8 (c) 2<r<8 (d) 25r58 (1994) | 11 |

181 | The set of points ( (x, y) ) whose distance from the line ( y=2 x+2 ) is the same as the distance from (2,0) is a parabola. This parabola is congruent to the parabola in standard form ( y=K x^{2} ) for some ( K ) which is equal to A ( frac{sqrt{5}}{12} ) в. ( frac{sqrt{5}}{4} ) c. ( frac{4}{sqrt{5}} ) D. ( frac{12}{sqrt{5}} ) | 11 |

182 | The differential equation ( (3 x+4 y+ ) 1) ( boldsymbol{d} boldsymbol{x}+(boldsymbol{4} boldsymbol{x}+boldsymbol{5} boldsymbol{y}+mathbf{1}) boldsymbol{d} boldsymbol{y}=boldsymbol{0} ) represents a family of A. Circles B. Parabolas c. Ellipses D. Hyperbolas | 11 |

183 | Draw the circles whose equation are ( 3 x^{2}+3 y^{2}=4 x ) | 11 |

184 | 46. Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is (1) 5 cm (2) 6.25 cm (3) 6 cm (4) 7.35 cm | 11 |

185 | The graph of ( x^{2}-4 x+y^{2}+6 y=0 ) in the xy-plane is a circle. What is the radius of the circle? | 11 |

186 | ( frac{x^{2}}{r^{2}-r-6}+frac{y^{2}}{r^{2}-6 r+5}=1 ) will represents the ellipse, if r lies in the interval: This question has multiple correct options B. ( (3, infty) ) ( c cdot(5, infty) ) D. ( (1, infty) ) | 11 |

187 | If the latus rectum of an ellipse ( boldsymbol{x}^{2} tan ^{2} varphi+boldsymbol{y}^{2} sec ^{2} varphi=1 ) is ( 1 / 2 ) then ( varphi ) is ( mathbf{A} cdot pi / 2 ) в. ( pi / 6 ) c. ( pi / 3 ) D. ( 5 pi / 12 ) | 11 |

188 | The centre of a circle is (2,-3) and the circumference is ( 10 pi . ) Then, the equation of the circle is A. ( x^{2}+y^{2}+4 x+6 y+12=0 ) B . ( x^{2}+y^{2}-4 x+6 y+12=0 ) c. ( x^{2}+y^{2}-4 x+6 y-12=0 ) D. ( x^{2}+y^{2}-4 x-6 y-12=0 ) | 11 |

189 | General second degree equation in ( x ) and ( y ) is ( a x^{2}+2 h x y+b y^{2}+2 g x+ ) ( 2 f y+c=0, ) Where ( a, h, b, g, f ) and ( c ) are constats. Prove that condition for it to be a circle | 11 |

190 | he centre of the circle passing through (0,0) and (1,0) and touching the circle x2+y2=9 is [2002] (a) (31) (b) (2.-13) (21) (a) (2) mation of | 11 |

191 | The axis of the parabola ( x^{2}-4 x-y+ ) ( mathbf{1}=mathbf{0} ) is A ( cdot y=-3 ) B. x=-3 c. ( x=2 ) D. none of these | 11 |

192 | The eccentricity of the ellipse ( 9 x^{2}+ ) ( 25 y^{2}-18 x-100 y-116=0, ) is A ( .25 / 16 ) в. ( 4 / 5 ) c. ( 16 / 25 ) D. ( 5 / 4 ) | 11 |

193 | The equation of the latus rectum of the parabola ( boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} ) is – ( A cdot 3 y=2 ) B. ( 2 y+3=0 ) c. ( 2 y=3 ) D. ( 3 y+2=0 ) | 11 |

194 | Find the equation of the ellipse whose vertices are ( (pm mathbf{5}, mathbf{0}) ) and foci are ( (pm mathbf{3}, mathbf{0}) ) | 11 |

195 | If the eccentricity of an ellipse is ( frac{5}{8} ) and the distance between its foci is ( 10, ) then its latus rectum is A ( cdot frac{39}{4} ) B. 12 c. 15 D. ( frac{37}{2} ) | 11 |

196 | 6. Let P be the point (1,0) and Q a point on the locus y = 8x. The locus of mid point of PQ is [2005] (a) y2 – 4x+2=0 (b) y2 +4x+2=0 (C) x² +4y+2=0 (d) x2 – 4y+2=0 | 11 |

197 | If ( e_{1} ) and ( e_{2} ) are the eccentricities of ( a ) hyperbola ( 3 x^{2}-3 y^{2}=25 ) and its conjugate respectively, then A ( cdot e_{1}^{2}+e_{2}^{2}=2 ) B . ( e_{1}^{2}+e_{2}^{2}=4 ) ( mathbf{c} cdot e_{1}+e_{2}=4 ) D. ( e_{1}+e_{2}=sqrt{2} ) | 11 |

198 | Equation of the parabola whose vertex is (0,0) and focus is the point of intersection of the lines ( boldsymbol{x}+boldsymbol{y}= ) ( 2,2 x-y=4 ) is A ( cdot y^{2}=2 x ) в. ( y^{2}=4 x ) c. ( y^{2}=8 x ) D . ( x^{2}=8 y ) | 11 |

199 | If the lines ( 2 x+3 y+1=0 ) and ( 3 x- ) ( mathbf{y}-mathbf{4}=mathbf{0} ) lie along diameters of a circle of circumference ( 10 pi, ) then the equation of the circle is: A ( cdot x^{2}+y^{2}-2 x+2 y-23=0 ) B. ( x^{2}+y^{2}-2 x-2 y-23=0 ) C. ( x^{2}+y^{2}+2 x+2 y-23=0 ) D. ( x^{2}+y^{2}+2 x-2 y-23=0 ) | 11 |

200 | 1 Let a circle be given by 2x(x -a) + y(2y-b)=0,(a + 0, 5 0 ). Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from | 11 |

201 | Find the equation of the parabola that satisfies the following conditions: Focus (0,-3)( ; ) directrix ( y=3 ) | 11 |

202 | The difference between the length ( 2 a ) of the transverse axis of a hyperbola of eccentricity ( e ) and the length of its latus rectum is : A ( cdot 2 aleft|3-e^{2}right| ) В ( cdot 2 aleft|2-e^{2}right| ) c. ( 2 aleft(e^{2}-1right) ) D. ( aleft(2 e^{2}-1right) ) | 11 |

203 | -* The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x2 + y2 = 9 is (2012) (a) 20(x2 + y2) – 36x +45 y=0 (b) 20 (x2 + y2) + 36x – 45 y=0 (C) 36(x2 + y2) – 20x +45 y | 11 |

204 | State whether the following statements are true or false. The equation ( x^{2}+y^{2}+2 x-10 y+ ) ( mathbf{3 0}=mathbf{0} ) represents the equation of a circle. A . True B. False | 11 |

205 | If a circle passes through the point (a, b) and cuts the circle x + y2 = k orthogonally, then the equation of the locus of its centre is (1988 – 2 Marks) (a) 2ax + 2by – (a? +62 +62) = 0 (b) 2ax + 2by – (a? – b2 + k_) = 0 (C) x2 + y2 – 3ax – 4by+(a? +62 – K2) = 0 (d) x2 + y2 – 2ax – 3by +(22 -62 – k) = 0. | 11 |

206 | What is the eccentricity of the conic ( 4 x^{2}+9 y^{2}=144 ) A ( frac{sqrt{5}}{3} ) в. ( frac{sqrt{5}}{6} ) c. ( frac{3}{sqrt{5}} ) D. ( frac{2}{3} ) | 11 |

207 | Find the equation of a circle if: (i)center ( (a, b) ) and radius ( sqrt{a^{2}+b^{2}} ) (ii)center ( (a sec alpha, b tan alpha) ) and radius ( sqrt{a^{2} sec ^{2} alpha+b^{2} sec ^{2} alpha} ) | 11 |

208 | Find the equation of the ellipse whose foci are ( (mathbf{0}, pm mathbf{6}) ) and length of the minor axis is 16 | 11 |

209 | ( frac{x^{2}}{8-a}+frac{y^{2}}{a-2}=1 ) represents an ellipse.Then find range of ‘a’ | 11 |

210 | The equation of parabola whose latus rectum is 2 units, axis is ( x+y-2=0 ) and tangent at the vertex is ( x-y+ ) ( 4=0 ) is given by A ( cdot(x+y-2)^{2}=4 sqrt{2}(x-y+4)^{2} ) B . ( (x-y-4)^{2}=4 sqrt{2}(x+y-2) ) C. ( (x+y-2)^{2}=2 sqrt{2}(x-y+4) ) D. ( (x-y-4)^{2}=2 sqrt{2}(x-y+2)^{2} ) | 11 |

211 | The equation of the hyperbola whose foci are ( (mathbf{6}, mathbf{5}),(-mathbf{4}, mathbf{5}) ) and eccentricity ( mathbf{5} / mathbf{4} ) is? A ( cdot frac{(x-1)^{2}}{16}-frac{(y-5)^{2}}{9}=1 ) В. ( frac{x^{2}}{16}-frac{y^{2}}{9}=1 ) c. ( frac{(x-1)^{2}}{16}-frac{(y-5)^{2}}{9}=-1 ) D. ( frac{(x-1)^{2}}{4}-frac{(y-5)^{2}}{9}=1 ) | 11 |

212 | The the focal distance of an end of the minor axis of any ellipse (reffered to its axes of ( x ) and ( y ) respectively) is ( k ) and the distance between the foci is ( 2 h ) then its equation is: A ( cdot frac{x^{2}}{k^{2}}+frac{y^{2}}{k^{2}+h^{2}}=1 ) B. ( frac{x^{2}}{k^{2}}+frac{y^{2}}{h^{2}-k^{2}}=1 ) ( ^{mathrm{C}} cdot frac{x^{2}}{k^{2}}+frac{y^{2}}{k^{2}-h^{2}}=1 ) D. ( frac{x^{2}}{k^{2}}+frac{y^{2}}{h^{2}}=1 ) | 11 |

213 | Find the locus of coordinates of ( A ) and ( B ) which are two points in place so that ( boldsymbol{P A}-boldsymbol{P B}= ) constant. | 11 |

214 | Find the eccentricity and length of latus rectum of the ellipse ( 9 x^{2}+16 y^{2}- ) ( 36 x+32 y-92=0 ) | 11 |

215 | In parabola ( y^{2}=18 x ) find the point where the ordinate is equal to three times the abscissa. | 11 |

216 | The graph of the equation ( x^{2}+frac{y^{2}}{4}=1 ) is A. an ellipse B. a circle c. a hyperbola D. a parabola E. two straight lines | 11 |

217 | A circle is given by x2 + (y-1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S) (a) {(x, y): x2 = 4y} {(x,y): y=0} (b) {(x, y): x2 + (y – 1)2 = 4}U {(x, y): y 50} (c) {(x, y): x2=y} U{(0,y):y>0} (d) {(x, y): x2 = 4y} {(0,y):y s0} | 11 |

218 | Find the equation of parabola with focus (5,0) and vertex (5,3) A ( cdot y=12(x-5)^{2}-3 ) B . ( y-3=-(x-5)^{2} ) c. ( y=frac{(x-5)^{2}}{12}-3 ) D. ( y=-frac{(x-5)^{2}}{12}+3 ) | 11 |

219 | Find the equation of the hyperbola satisfying the give conditions: Vertices ( (pm mathbf{7}, mathbf{0}) ) ( e=frac{4}{3} ) | 11 |

220 | Coordinates of the focus of the parabola ( x^{2}-4 x-8 y-4=0 ) are A ( .(0.2) ) B. (2,1) c. (1,2) D. (-2,-1) | 11 |

221 | The length of latus rectum of the hyperbola ( 4 x^{2}-9 y^{2}-16 x-54 y- ) ( mathbf{1 0 1}=mathbf{0} ) is ( A cdot frac{8}{5} ) B. ( frac{8}{7} ) ( c cdot frac{8}{9} ) D. ( frac{8}{3} ) | 11 |

222 | Find the equation of the ellipse whose vertices are ( (pm mathbf{7}, mathbf{0}) ) and foci are ( (pm mathbf{4}, mathbf{0}) ) | 11 |

223 | The foci of the ellipse ( frac{x^{2}}{16}+frac{y^{2}}{b^{2}}=1 ) and the hyperbola ( frac{x^{2}}{144}-frac{y^{2}}{81}=frac{1}{25} ) coincide then the value of ( b^{2} ) is: A . 5 B. 7 c. 9 D. 4 | 11 |

224 | The length of the latus rectum of the ( operatorname{conic} frac{5}{r}=3-2 cos theta ) is A ( cdot frac{3}{5} ) B. ( frac{5}{3} ) ( c cdot frac{6}{5} ) D. ( frac{10}{3} ) | 11 |

225 | Find the centre and radius of the circle ( x^{2}+y^{2}=36 ) | 11 |

226 | The equation of the circle which touches the lines ( x=0, y=0 ) and ( 4 x+3 y=12 ) is A ( cdot x^{2}+y^{2}-2 x-2 y-1=0 ) В . ( x^{2}+y^{2}-2 x-2 y+3=0 ) c. ( x^{2}+y^{2}-2 x-2 y+2=0 ) D. ( x^{2}+y^{2}-2 x-2 y+1=0 ) E . ( x^{2}+y^{2}-2 x-2 y-3=0 ) | 11 |

227 | Match the Column The answers to these questions have to be appropriately doubled | 11 |

228 | Find the equation of the ellipse whose foci are ( (mathbf{0}, pm mathbf{6}) ) and length of the minor axis is 22 | 11 |

229 | Find the lengths of, and the equations to, the focal radii drawn to the point ( (4 sqrt{3}, 5) ) of the ellipse ( 25 x^{2}+16 y^{2}= ) ( mathbf{1 6 0 0} ) | 11 |

230 | Find the equation of the hyperbola satisfying the give conditions: Vertices (0,±5) foci (0,±8) | 11 |

231 | The equation of the latus rectum of the ellipse ( 9 x^{2}+4 y^{2}-18 x-8 y-23=0 ) are A ( . y=pm sqrt{5} ) B ( cdot y=-sqrt{5} ) c. ( y=1 pm sqrt{5} ) D. ( y=-1 pm sqrt{5} ) | 11 |

232 | The equation ( sqrt{(x-2)^{2}+y^{2}}+ ) ( sqrt{(x+2)^{2}+y^{2}}=5 ) represents A . a circle B. ellipse c. line segment D. an empty set | 11 |

233 | If the two circles (x – 1)2 + (y – 3)2 = r- and x + y2 – 8x +2y +8=0 intersect in two distinct po sect in two distinct points, then (1989- 2 Marks) (a) 2<r<8 (b) r2 1 | 11 |

234 | An ellipse with foci (2,2),(3,-5) passes through ( (6,-1), ) then its semilatus rectum is: ( A cdot frac{7}{2} ) в. ( frac{5}{2} ) ( c cdot frac{9}{2} ) D. ( frac{11}{2} ) | 11 |

235 | Find vertex and focus for the equation ( boldsymbol{y}^{2}-mathbf{8} boldsymbol{y}-boldsymbol{x}+mathbf{1} boldsymbol{9}=mathbf{0} ) | 11 |

236 | 4 17. Consider a family of circles which tamily of circles which are passing through the point (1, 1) and are tangent to x-axis. ” coordinate of the centre of the circles, then the set ol of k is given by the interval [2007] tangent to x-axis. If (h, k) are the of the circles, then the set of values (a) — Sk (b) ks VIN (C) 0 <k (d) kz | 11 |

237 | The equation of the hyperbola with vertices (0,±15) and foci (0,±20) is A ( cdot frac{x^{2}}{175}-frac{y^{2}}{225}=1 ) В. ( frac{x^{2}}{625}-frac{y^{2}}{125}=1 ) c. ( frac{y^{2}}{225}-frac{x^{2}}{125}=1 ) D. ( frac{y^{2}}{225}-frac{x^{2}}{175}=1 ) | 11 |

238 | Consider a rigid square ( A B C D ) as in the figure with ( A ) and ( B ) on the ( x ) and ( y ) axis respectively. When ( A ) and ( B ) slide along their respective axes, the locus of ( C ) forms a part of A. A circle B. A parabola C. A hyperbola D. An ellipse which is not a circle | 11 |

239 | O and 2x – 3y-5=0 are two Stt Square units, the equation [2006] 15. If the lines 3r-47-7=0 and 2x – 3y – diameters of a circle of area 491 square un of the circle is (a) x2 + y2 + 2x – 2y – 47 = 0 (b) x2 + y2 + 2x – 2y – 62 = 0 (c) x2 + y2 – 2x + 2y -62 = 0 (d) x² + y2 –2x+2y – 47 = 0 6. La | 11 |

240 | Find the length of the latus rectum, the eccentricity and the coordinates of the foci of the ellipse ( mathbf{5} boldsymbol{x}^{2}+mathbf{4} boldsymbol{y}^{2}=mathbf{1} ) | 11 |

241 | The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x – 6y +9 sin? a +13 cos2 a=0 is 2a. The equation of the locus of the point Pis (1996 – 1 Mark) (a) x2 + y2 + 4x – 6y + 4 =0 (b) x2 + y2 + 4x – 6y-9=0 (C) x2 + y2 + 4x – 6y-4=0 (d) x2 + y2 + 4x – 6y +9=0 | 11 |

242 | Which ordered number pair represents the center of the circle ( x^{2}+y^{2}-6 x+ ) ( 4 y-12=0 ? ) ( A cdot(9,4) ) B. (3,2) ( c cdot(3,-2) ) ( D cdot(6,4) ) | 11 |

243 | Find the eccentricity of an ellipse in which distance between the foci is 10 and that of focus and corresponding directrix is 15 A ( cdot frac{1}{4} ) B. ( frac{1}{2} ) c. 1 D. ( frac{3}{4} ) | 11 |

244 | Let P be the point on the parabola, y = 8x W Which on the parabola, y2 = 8x which is at a ce from the centre Cofthe circle, x2 +(y+6 =1. n of the circle, passing through Cand having [JEEM 2016] & the minimum distance from the centre Then the equation of the circle, passin its centre at P is: (a) x² + y2 -*+2y-24 =0 (b) x2 + y2 – 4x +9y+18=0 (c) x2 + y2-4x+8y+12=0 (d) x2 + y2 -x+4y-12=0 | 11 |

245 | Find the focus of the parabola ( boldsymbol{y}= ) ( -2(x+4)^{2}-1 ) ( mathbf{A} cdot(-4,-1) ) в. ( left(-4, frac{9}{8}right) ) c. (-4,1) D. ( left(-4,-frac{9}{8}right) ) | 11 |

246 | Find the equation of the ellipse whose vertices are ( (pm mathbf{9}, mathbf{0}) ) and foci are ( (pm mathbf{5}, mathbf{0}) ) | 11 |

247 | 7. Let a given line L, intersects the x and y axes at P and Q. respectively. Let another line L, perpendicular to L, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin (1987- 3 Marks) | 11 |

248 | 16. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008] (a) (0,2) (b) (1,0) (c) (0,1) (d) (2,0) | 11 |

249 | The sum of the distances of any point on the ellipse ( 3 x^{2}+4 y^{2}=24 ) from its foci is : ( A cdot 8 sqrt{2} ) B. 8 c. ( 16 sqrt{2} ) D. ( 4 sqrt{2} ) | 11 |

250 | If the latusrectum of an ellipse is equal to half of minor axis, find its eccentricity. | 11 |

251 | 15. If the circles x2 + y2 + 2x + 2ky + 6 = 0 ne circles x2 + y2 + 2x + 2ky+6=0. x2 + y2 + 2ky + k=0 intersect orthogonally, then k is (20005) (2) 2017 (6) 2012 (1) 2017 / (2) – 208 2 / 2 | 11 |

252 | ( 2 x^{2}+y^{2}-8 x-2 y+1=0 ) Find the square of the Latus Rectum for the given ellipse. | 11 |

253 | 7. Let a given line L, intersects the x and y axes at P and Q, respectively. Let another line L2, perpendicular to L,, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin. (1987 – 3 Marks) | 11 |

254 | 36. If the tangent at (1, 7) to the curve x2 = y-6 touches the circle x² + y2 +16x +12y+c=0 then the value of cis : JEEM 2018 (a) 185 (b) 85 (3) 95 (4) 195 | 11 |

255 | The equation ( frac{x^{2}}{10-a}+frac{y^{2}}{4-a}=1 ) represents an ellipse if ( mathbf{A} cdot a4 ) c. ( 4<a<10 ) D. None of these | 11 |

256 | entres of a set of circles, each of radius 3, lie on the 12+12=25. The locus of any point in the set is (b) x2+y2 <25 [2002] (c) x²+ y = 25 (d) 3 < x² + y² <9 chironi 6 (a) 4<x²+77 < 64 | 11 |

257 | Eccentricity of the ellipse ( 4 x^{2}+y^{2}-8 y-8=0 ) is A ( frac{sqrt{3}}{2} ) в. ( frac{sqrt{3}}{4} ) ( c cdot frac{sqrt{3}}{sqrt{2}} ) D. ( frac{sqrt{3}}{8} ) E ( cdot frac{sqrt{3}}{16} ) | 11 |

258 | A straight line drawn through the common focus ( mathrm{S}^{prime} ) of a number of conics meets them in the points ( P_{1}, P_{2}, ldots ; ) on it is taken a point ( Q ) such that the reciprocal of ( mathrm{SQ} ) is equal to the sum of the reciprocals of ( S P_{1}, S P_{2}, ldots ) Prove that the locus of ( Q ) is a conic section whose focus is ( 0, ) and show that the reciprocal of its latus rectum is equal to the sum of the reciprocals of the latera recta of the given conics. | 11 |

259 | Find the inclinations of the axes so that the following equations may represent circles, and in each case find the radius and centre; ( boldsymbol{x}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}-2 boldsymbol{g} boldsymbol{x}-boldsymbol{2} boldsymbol{f} boldsymbol{y}=mathbf{0} ) | 11 |

260 | A parabola has ( x ) – axis as its axis, ( y ) axis as its directrix and ( 4 a ) as its latus rectum. If the focus lies to the left side of the directrix then the equation of the parabola is ( mathbf{A} cdot y^{2}=4 a(x+a) ) B ( cdot y^{2}=4 a(x-a) ) C ( cdot y^{2}=-4 a(x+a) ) D ( cdot y^{2}=4 a(x-2 a) ) | 11 |

261 | For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum. ( x^{2}=6 y ) | 11 |

262 | The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the ( x ) axis A .2 B. 1 ( c .3 ) D. 4 | 11 |

263 | The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 – 6x — 8y= 24 is (1998 – 2 Marks) (a) o (6) 1 (c) 3 (d) 4 | 11 |

264 | In an ellipse the distance between the foci is one third of the distance between the directrices, then its ( e ) is A ( cdot frac{1}{2} ) B. ( frac{1}{sqrt{3}} ) ( c cdot frac{2 sqrt{2}}{3} ) D. ( frac{1}{3} ) | 11 |

265 | If (2,4) and (10,10) are the ends of a latus – rectum of an ellipse with eccentricity ( frac{1}{2}, ) then the length of semi major axis is A ( cdot frac{20}{3} ) в. ( frac{15}{3} ) c. ( frac{40}{3} ) D. None of these | 11 |

266 | 1. Find the equation of the circle whose radius is 5 and which touches the circle x2 + y2 – 2x – 4y-20=0 at the point (5,5). (1978) | 11 |

267 | The graph between ( log left(theta-theta_{0}right) ) and time ( (t) ) is a straight line in the experiment based on Newton’s law cooling. What is the shape of graph between ( theta ) and ( t ? ) A. A straight line B. A parabola c. A hyperbola D. A circle | 11 |

268 | 52. The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm. The length of the transverse common tangent to the circles is : (1) 12 cm (2) 6.76 cm (3) 7/6 cm (4) 18 cm | 11 |

269 | IS of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from positive x-axis then which of the following points does not lie on it? JEE M 2019-9 Jan (ML (a) (5,256) (b) (8,6) (C) (6, 412) (d) (4, -4) | 11 |

270 | The asymptotes of a hyperbola ( 4 x^{2}- ) ( 9 y^{2}=36 ) are A. ( 2 x pm 3 y=1 ) в. ( 2 x pm 3 y=0 ) c. ( 3 x pm 2 y=1 ) D. None | 11 |

271 | The equation of hyperbola whose coordinates of the foci are (±8,0) and the lenght of latus rectum is 24 units, is A ( cdot 3 x^{2}-y^{2}=48 ) в. ( 4 x^{2}-y^{2}=48 ) c. ( x^{2}-3 y^{2}=48 ) D. ( x^{2}-4 y^{2}=48 ) | 11 |

272 | The latus rectum of a parabola whose focal chord is ( P S Q ) such that ( S P=3 ) and ( S Q=2, ) is given by A ( cdot frac{24}{5} ) в. ( frac{12}{5} ) ( c cdot frac{6}{5} ) D. ( frac{48}{5} ) | 11 |

273 | The equation of circle with its centre at the origin is ( boldsymbol{x}^{2}+boldsymbol{y}^{2}=boldsymbol{r}^{2} ) A. True B. False c. Neither D. Either | 11 |

274 | Find the equation of the ellipse whose vertices are ( (pm mathbf{5}, mathbf{0}) ) and foci are (±1,0) | 11 |

275 | 41. If one end of a focal chord of the parabola, y = (1.4), then the length of this focal chord is: [JEE M 2019-9 April (M)). (a) 25 (6) 22 (c) 24 (d) 20 | 11 |

276 | ( P ) and ( Q ) are the foci of the ellipse ( frac{x^{2}}{a^{2}}+ ) ( frac{y^{2}}{b^{2}}=1 ) and ( B ) is an end of the minor axis. If ( triangle P B Q ) is an equilateral triangle, the eccentricity of the ellipse is: A ( cdot frac{1}{sqrt{2}} ) в. ( frac{1}{3} ) ( c cdot frac{1}{2} ) D. ( frac{sqrt{3}}{2} ) | 11 |

277 | If the angle between the lines joining the end points of minor axis of an ellipse with its foci is ( frac{pi}{2}, ) then the eccentricity of the ellipse is A ( cdot frac{1}{2} ) в. ( frac{1}{sqrt{2}} ) c. ( frac{sqrt{3}}{2} ) D. ( frac{1}{2 sqrt{2}} ) | 11 |

278 | The point to which the axes are to be translated to eliminate ( x ) and ( y ) terms in the equation ( 3 x^{2}-4 x y-2 y^{2}-3 x- ) ( 2 y-1=0 ) is ( ^{mathrm{A}} cdotleft(frac{5}{2}, 3right) ) в. ( left(-4, frac{3}{2}right) ) c. (-2,3) D. (2,3) | 11 |

279 | An ellipse has its centre at (1,-1) and semi-major axis ( =8 ) and it passes through the point ( (1,3) . ) The equation of the ellipse is A ( cdot frac{(x+1)^{2}}{64}+frac{(y+1)^{2}}{16}=1 ) в. ( frac{(x-1)^{2}}{64}+frac{(y+1)^{2}}{16}=1 ) c. ( frac{(x-1)^{2}}{16}+frac{(y+1)^{2}}{64}=1 ) D. ( frac{(x+1)^{2}}{64}+frac{(y-1)^{2}}{16}=1 ) | 11 |

280 | A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x +2y=6 at Pand Q. Prove that the tangents at P and Qof the ellipse x2 + 2y2 = 6 are at right angles. (1997 – 5 Marks) | 11 |

281 | 22. The equation of the circle passing through the foci of the ellipse – = 1, and having centre at (0, 3) is 16 (a) x2 + y2 – 6y – 7=0 (C) x2 + y2 – 6y – 5 = 0 (JEE M 2013 (b) x2 + y2 – 6y +7=0 (d) x2 + y2 – 6y +5 = 0 | 11 |

282 | If ( (a, b) ) lies on circle with centre as origin, then its radius will be A ( . a-b ) B. ( a+b ) c. ( sqrt{a^{2}+b^{2}} ) D. ( a^{2}+b^{2} ) | 11 |

283 | Circles are described on the major axis and the line joining the foci of the ellipse ( 3 x^{2}+2 y^{2}=6 ) as diameters. Then the radii of the circles are in the ratio: A ( cdot sqrt{2}: 1 ) B. ( sqrt{3}: 1 ) ( c .3: 2 ) D. 5: 4 | 11 |

284 | 14. I The equation of the circle passing through (1, 1) and points of intersection of x2 + y2 + 13x – 3y = 2×2 + 2y2 + 4x – 7y-25=0 is (1983 – 1 Mark) (a) 4×2 + 4y2 – 30x – 10y-25=0 (b) 4×2 + 4y2 + 30x – 13y-25 = 0 (c) 4×2 + 4y2 – 17x – 10y +25=0 (d) none of these | 11 |

285 | Find the equation of the parabola with vertex (0,0) and focus at (-3,0) | 11 |

286 | 11. Consider the family of circles x2 + y2 = r2, 2<r<5. Ifin the first quadrant, the common taingent to a circle of this family and the ellipse 4×2 + 25y2 = 100 meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB. (1999 – 10 Marks) | 11 |

287 | 13. The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is [2007] (a) (2,4) (b) (-2,0) (c) (-1,1) (d) (0,2) | 11 |

288 | Find the equation of the circle drawn on the intercept made by the line ( 2 x+ ) ( 3 y=6 ) between the coordinate axes as diameter. | 11 |

289 | Centre of the hyperbola ( x^{2}+4 y^{2}+ ) ( 6 x y+8 x-2 y+7=0 ) is A ( .(1,1) ) в. (0,2) D. None of these | 11 |

290 | A point ( P ) on the ellipse ( frac{x^{2}}{25}+frac{y^{2}}{9}=1 ) has the eccentric angle ( frac{pi}{8} . ) The sum of the distance of ( P ) from the two foci is A . 5 B. 6 c. 10 D. 3 | 11 |

291 | Find the equation of the circle passing through the points (5,5),(3,7) and has its center on the line ( boldsymbol{x}-mathbf{4} boldsymbol{y}+mathbf{1 1}=mathbf{0} ) | 11 |

292 | For an ellipse with axes are coordinate axes, ( A ) and ( L ) are the ends of major axis and latusrectum respectively. Area of ( triangle O A L=8 s q . ) units and, ( e=frac{1}{sqrt{2}}, ) then equation of the ellipse is: ( ^{text {A }} cdot frac{x^{2}}{16}+frac{y^{2}}{8}=1 ) B. ( frac{x^{2}}{32}+frac{y^{2}}{16}=1 ) c. ( frac{x^{2}}{64}+frac{y^{2}}{32}=1 ) D. ( frac{x^{2}}{8}+frac{y^{2}}{4}=1 ) | 11 |

293 | 18. Tangent is drawn to parabola y2 – 2y – 4x + 5 = 0 at a point P which cuts the directrix at the point Q. A point R is such that it divides OP externally in the ratio 1/2 : 1. Find the lomne afnaint D (2011 Mantra) | 11 |

294 | For the function ( f(x)=a(x-h)^{2}+k ) which of the following statements is wrong? A. The value of ( a ) is negative B. ( f(x) ) is symmetrical across the line ( y=3 ) c. The function ( g(x)=frac{2 x}{3} ) intersects ( f(x) ) at its vertex D. The value of ( h ) is positive | 11 |

295 | The equation of ellipse with the length of major and minor axis as ( 12,16 mathrm{cm} ) respectively is | 11 |

296 | Which is not represented by quadratic equation? A . Circle B. Straight line c. Parabola D. Hyperbola | 11 |

297 | The foci of an ellipse are ( boldsymbol{S}(-1,-1), boldsymbol{S}^{prime}(0,-2) ) and its ( mathbf{e}=frac{1}{2} ) then the equation of the directrix corresponding to the focus ( S ) is : A. ( x-y+3=0 ) в. ( x-y+7=0 ) c. ( x-y+5=0 ) D. ( x-y+4=0 ) | 11 |

298 | Find the eccentricity of the conic represented by ( boldsymbol{x}^{2}-boldsymbol{y}^{2}-boldsymbol{4} boldsymbol{x}+boldsymbol{4} boldsymbol{y}+ ) ( mathbf{1 6}=mathbf{0} ) A ( cdot sqrt{2} ) B. ( sqrt{3} ) ( c cdot-sqrt{2} ) D. ( -sqrt{3} ) | 11 |

299 | The equation of a parabola which passes through the intersection of a straight line ( x+y=0 ) and the circle ( x^{2}+y^{2}+4 y=0 ) is. A ( cdot y^{2}=4 x ) В. ( y^{2}=x ) c. ( y^{2}=2 x ) D. None of these | 11 |

300 | The centre of the circle given by ( mathbf{r} cdot(mathbf{i}+ ) ( 2 mathbf{j}+2 mathbf{k})=15 ) and ( |mathbf{r}-(mathbf{j}+2 mathbf{k})|=mathbf{4} ) A ( .(0,1,2) ) в. (1,3,4) c. (-1,3,4) D. None of these | 11 |

301 | 16. ) TV-2X + 2y-47 = U Let C be the circle with centre (O, equation of the locus of the mid points of the cho ne circle with centre (0,0) and radius 3 units. The he mid points of the chords of the circle C that subtend an angle of 21 at its center is [2006] (a) x² + y² = 3 © x² + y2 = 27 (6) x² + y² =1 (a) x² + y2 = | 11 |

302 | The lines ( 2 x-3 y=5 ) and ( 3 x-4 y=7 ) are the diameters of a circle of area 154 square units. An equation of this circle is ( (boldsymbol{pi}=mathbf{2 2} / mathbf{7}) ) A ( cdot x^{2}+y^{2}+2 x-2 y=62 ) B. ( x^{2}+y^{2}+2 x-2 y=47 ) c. ( x^{2}+y^{2}-2 x+2 y=47 ) D. ( x^{2}+y^{2}-2 x+2 y=62 ) | 11 |

303 | A circle with center (3,8) contains the point ( (2,-1) . ) Another point on the circle is: в. (4,17) c. (5,-9) D. (7,15) E . (9,6) | 11 |

304 | The equations of the tangents drawn from the origin to the circle x2 + y2 – 2rx – 2hy + h2 = 0, are (1988 – 2 Marks) (a) x=0 (b) y=0 (c) (h2 – r2)x – 2rhy=0 (d) (h2 – p2)x+ 2rhy=0 | 11 |

305 | If the eccentricity of an ellipse is ( frac{5}{8} ) and the distance between its foci is ( 10, ) then find latus-rectum of the ellipse. | 11 |

306 | Eccentricity of the conic represented by ( boldsymbol{x}=frac{boldsymbol{e}^{boldsymbol{a}}+boldsymbol{e}^{-boldsymbol{a}}}{mathbf{2} sqrt{mathbf{3}}}, boldsymbol{y}=frac{boldsymbol{e}^{boldsymbol{a}}-boldsymbol{e}^{-boldsymbol{a}}}{mathbf{2}} ) is | 11 |

307 | Find the equation of the circle whose two end points of the diameter are (4,-2) and (-1,3) | 11 |

308 | Find the latus rectum of the parabola ( boldsymbol{x}^{2}+mathbf{2} boldsymbol{y}-mathbf{3} boldsymbol{x}+mathbf{5}=mathbf{0} ) ( mathbf{A} cdot mathbf{1} ) B . 2 ( c cdot 4 ) D. | 11 |

309 | Find the equation of the circle with centre (1,1) and radius ( sqrt{2} ) | 11 |

310 | A circle of radius 5 units touches the coordinate axes in the first quadrant. If the circle makes one complete roll on ( x ) axis along the positive direction of ( x ) axis, find its equation in new position. | 11 |

311 | The sum of the focal distances of a point on the ellipse ( frac{x^{2}}{4}+frac{y^{2}}{9}=1 ) is: A . 4 units B. 6 units c. 8 units D. 10 units | 11 |

312 | The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola ( frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1 ) is equal to (where ( e ) is the eccentricity of the hyperbola) A ( . ) be в. ( c cdot a b ) D. ( a ) | 11 |

313 | The eccentricity of the conic ( frac{mathbf{7}}{r}=mathbf{2}+ ) ( 3 cos theta ) is A . -3 в. 3 ( c cdot frac{3}{2} ) D. | 11 |

314 | The length of the latusrectum of an ellipse is equal to one-half of its minor axis. Then the eccentricity of the ellipse is : A ( cdot frac{sqrt{3}}{2} ) B. ( frac{sqrt{2}}{3} ) c. ( frac{1}{sqrt{3}} ) D. ( frac{1}{sqrt{2}} ) | 11 |

315 | What are represented by the equation ( boldsymbol{x}^{3}+boldsymbol{y}^{3}+(boldsymbol{x}+boldsymbol{y})(boldsymbol{x} boldsymbol{y}-boldsymbol{a} boldsymbol{x}-boldsymbol{a} boldsymbol{y})=mathbf{0} ) | 11 |

316 | For the conic ( 9 x^{2}-16 y^{2}+18 x+ ) ( 32 y-151=0, ) find ( e ) A ( cdot frac{5}{4} ) в. ( frac{4}{5} ) ( c cdot frac{1}{2} ) D. None of these | 11 |

317 | The eccentricity of the conic ( 9 x^{2}+ ) ( 25 y^{2}=225 ) is A ( cdot frac{2}{5} ) B. ( frac{4}{5} ) ( c cdot frac{1}{3} ) D. E. | 11 |

318 | Prove that the eccentricity of the conic given by the general equation satisfies the relation ( frac{e^{4}}{1-e^{2}}+4= ) ( frac{(a+b-2 h cos omega)^{2}}{left(a b-h^{2}right) sin ^{2} omega}, ) where ( omega ) is the angle between the axes. | 11 |

319 | If the normal at the end of latus rectum of the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) passes through ( (0,-b), ) then ( e^{4}+e^{2} ) (where ( E ) is eccentricity) equals A cdot eccentricity of the ellipse is ( sqrt{frac{sqrt{5}-1}{2}} ) B. ratio of the minor and major axes is ( frac{sqrt{5}+1}{2} ) c. square of the eccentricity is equal to the ratio of the minor and major axes D. none of these | 11 |

320 | 5. The abscissa of the two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of the equation x2 + 2px – q2 = 0. Find the equation and the radius of the circle with AB as diameter. (1984 – 4 Marks) | 11 |

321 | 10. A circle touches the line y = x at a point P such that OP= 412, where is the origin. The circle contains the point (-10, 2) in its interior and the length of its chord on the line x + y = 0 is 62. Determine the equation of the circle. (1990 – 5 Marks) | 11 |

322 | Find the equation to the ellipses, whose centres are the origin, whose axes are the axes of coordinates, and which pass through ( (alpha) ) the points ( (2,2), ) and (3,1) and ( (beta) ) the points (1,4) and (-6,1) | 11 |

323 | Find the equation of the ellipse referred to its centre whose foci are the points (4,0) and (4,0) and whose eccentricity is ( frac{1}{3} ) | 11 |

324 | Find the equation of the circle passing through the points (0,-1) and (2,0) and whose centre lies on the line ( 3 x+ ) ( boldsymbol{y}=mathbf{5} ) | 11 |

325 | Find the equation of the circle which pass through the origin and cut off intercepts ( a ) and ( b ) respectively from the ( x ) and ( y ) axes. | 11 |

326 | Find the value of ( a ) for which the ellipse ( frac{x^{2}}{y^{2}}+frac{y^{2}}{b^{2}}=1,(a>b), ) if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola ( x^{2}=-2(y-2) ) | 11 |

327 | If the eccentricity of an ellipse is ( frac{5}{8} ) and the distance between its foci is ( 10, ) then find the latusrectum of the ellipse. | 11 |

328 | If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity. | 11 |

329 | 28. Consider a branch of the hyperbola x2 – 2y2 – 2V3x – 4/2y—6= 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (2008) | 11 |

330 | The length of the latus rectum of the parabola ( boldsymbol{x}=boldsymbol{a} boldsymbol{y}^{2}+boldsymbol{b} boldsymbol{y}+boldsymbol{c} ) is ( frac{boldsymbol{k}}{boldsymbol{a}} . ) Find ( boldsymbol{k} ) | 11 |

331 | An ellipse, with foci at (0,2) and (0,-2) and mirror axis of length ( 4, ) passes through which of the following points? A ( cdot(1,2 sqrt{2}) ) B. ( (2, sqrt{2}) ) D. ( (sqrt{2}, 2) ) | 11 |

332 | Trace the following central conics. ( boldsymbol{x} boldsymbol{y}-boldsymbol{y}^{2}=boldsymbol{a}^{2} ) | 11 |

333 | On the ellipse, ( 9 x^{2}+25 y^{2}=225, ) find the point whose distance to the focus ( F_{1} ) is four times the distance to the other focus ( boldsymbol{F}_{2} ) ( mathbf{A} cdot[-15, sqrt{63}] ) ( ^{text {В }} cdotleft(frac{-15}{4}, frac{sqrt{63}}{2}right) ) ( ^{mathrm{c}} cdotleft(frac{-15}{4}, frac{sqrt{63}}{4}right) ) D. ( left(frac{-15}{2}, frac{sqrt{63}}{2}right) ) | 11 |

334 | 29. The line passing through the extremity A of the major avis and extremity B of the minor axis of the ellipse x2 +9y2=9 . meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, Mand the origin Ois (2009) 31 ZI (b) 10 () 10 (d) 27 | 11 |

335 | The equation of the ellipse whose foci ( operatorname{are}(pm 5,0) ) and of the directrix is ( 5 x= ) ( 36, ) is A ( frac{x^{2}}{36}+frac{y^{2}}{11}=1 ) B. ( frac{x^{2}}{6}+frac{y^{2}}{sqrt{11}}=1 ) c. ( frac{x^{2}}{6}+frac{y^{2}}{11}=1 ) D. None of these | 11 |

336 | Find the equation of normal to the parabola ( y^{2}=4 a x ) which passes through the point ( (-6 a, 0) ). and suspended at ( 60^{circ} ) | 11 |

337 | Find the co-ordinates of the foci, the vertices, the length of major axis, latus rectum and the eccentricity of the conic represented by the equation ( 3 x^{2}+ ) ( 5 y^{2}=15 ) | 11 |

338 | An ellipse has ( O B ) as semi-minor axis, ( F ) and ( F^{prime} ) its foci and the ( angle F B F^{prime} ) is a right angle. Then, the eccentricity of the ellipse is A ( cdot frac{1}{sqrt{3}} ) B. ( frac{1}{4} ) ( c cdot frac{1}{2} ) D. ( frac{1}{sqrt{2}} ) | 11 |

339 | Find ( a ) and ( b ) for the ellipse ( b^{2} x^{2}+ ) ( a^{2} y^{2}=a^{2} b^{2} ) if the distance between the directrices is ( 5 sqrt{5} ) and the distance between the foci is ( 4 sqrt{5} ). Give answer to the nearest integer | 11 |

340 | If the eccentricity of a hyperbola is ( frac{5}{4} ) then find the eccentricity of its conjugate hyperbola. | 11 |

341 | 5. The abscissa of the two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of the equation x2 + 2px – q2 = 0. Find the equation and the radius of the circle with AB as diameter. (1984 – 4 Marks) | 11 |

342 | Find the equation to the parabola whose focus is (1,-1) and vertex is (2,1) | 11 |

343 | Find the equation of the circle which passes through (2,3) and (4,5) and the centre lies on the straight line ( y- ) ( 4 x+3=0 ) | 11 |

344 | A parabola with axis parallel to ( x ) axis passes through ( (mathbf{0}, mathbf{0}),(mathbf{2}, mathbf{1}),(mathbf{4},-mathbf{1}) . ) Its length of latus rectum is A ( cdot frac{2}{3} ) B. ( c cdot frac{7}{3} ) D. ( frac{1}{3} ) | 11 |

345 | The foci of the hyperbola ( 16 x^{2}-9 y^{2}- ) ( 64 x+18 y-90=0 ) are ( ^{mathrm{A}} cdotleft(frac{24 pm 5 sqrt{145}}{12}, 1right) ) B. ( left(frac{21 pm 5 sqrt{145}}{12}, 1right) ) c. ( left(1, frac{24 pm 5 sqrt{145}}{2}right) ) D ( cdotleft(1, frac{21 pm 5 sqrt{145}}{2}right) ) E ( cdotleft(frac{21 pm 5 sqrt{145}}{2},-1right) ) | 11 |

346 | Find the equation of the circle with center at (-3,5) and passes through the point (5,-1) A ( cdot(x+3)^{2}+(y-5)^{2}=100 ) B. ( (x-3)^{2}+(y-5)^{2} ) C. ( (x+3)^{2}+(y-5)^{2} ) D. None of the above | 11 |

347 | Find the equation of parabola whose focus is ( S(1,-7) ) and vertex is ( boldsymbol{A}(mathbf{1},-mathbf{2}) ) | 11 |

348 | The length of latus rectum of the parabola ( (x-2 a)^{2}+y^{2}=x^{2} ) is A ( .2 a ) B. ( 3 a ) ( c cdot 6 a ) D. ( 4 a ) | 11 |

349 | Find the equation of the circle circumscribing a square ABCD with side I and ( A B ) and ( A D ) as coordinate axes | 11 |

350 | The equation of the image of the circle ( x^{2}+y^{2}-6 x-4 y+12=0 ) by the line mirror ( boldsymbol{x}+boldsymbol{y}-mathbf{1}=mathbf{0} ) is A ( cdot x^{2}+y^{2}+2 x+4 y+4=0 ) B . ( x^{2}+y^{2}-2 x+4 y+4=0 ) c. ( x^{2}+y^{2}+2 x+4 y-4=0 ) D. ( x^{2}+y^{2}+2 x-4 y+4=0 ) | 11 |

351 | The point (3,4) is the focus and ( 2 x- ) ( 3 y+5=0 ) is the directrix of a parabola. Lenghth of latus rectum is A ( cdot frac{2}{sqrt{13}} ) в. ( frac{4}{sqrt{13}} ) c. ( frac{1}{sqrt{13}} ) D. ( frac{3}{sqrt{13}} ) | 11 |

352 | The equation of ellipse whose major axis is along the direction of ( x ) -axis, eccentricity is ( e=2 / 3 ) A ( cdot 36 x^{2}+20 y^{2}=405 ) B . ( 20 x^{2}+36 y^{2}=405 ) c. ( 30 x^{2}+22 y^{2}=411 ) D. ( 22 x^{2}+32 y^{2}=409 ) | 11 |

353 | The focus of an ellipse is at the origin. The directrix is the line ( x=4 ) and its eccentricity is ( frac{1}{2} ) then length of its semi major axis is A ( cdot frac{2}{3} ) B. ( frac{4}{3} ) ( c cdot frac{5}{3} ) D. ( frac{8}{3} ) | 11 |

354 | 58 The tangent PT and the normal PNT at a point P on it meet its axis at The locus of the centroid of the trian whose ormal PN to the parabola y2 =4ax S axis at points T and N, respectively. d of the triangle PTN is a parabola (2009) (a) vertex is (b) directrix is x=0 (©) latus rectum is a (d) focus is (a,0) | 11 |

355 | The parabola ( (boldsymbol{y}+mathbf{1})^{2}=boldsymbol{a}(boldsymbol{x}-boldsymbol{2}) ) passes through the point (1,-2) then the equation of its directrix is A ( .4 x+1=0 ) B. ( 4 x-1=0 ) ( mathbf{c} cdot 4 x+9=0 ) D. ( 4 x-9=0 ) | 11 |

356 | 10. Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is (20015) (a) a parabola (b) a circle (c) an ellipse (d) a pair of straight lines | 11 |

357 | 1. The number of values of c such that the straight line y= 4x+c touches the curve (x2/4) + y2 = 1 is (1998 – 2 Marks) (a) 0 (b) 1 (c) 2 (d) infinite. | 11 |

358 | If ( mathbf{S} ) and ( mathbf{S}^{prime} ) are the foci and ( mathbf{B} ) is an endpoint of the minor axis of an ellipse. If ( angle S B S^{prime}=120^{circ} ) then its eccentricity is: A ( cdot frac{sqrt{5}}{2} ) B. ( frac{sqrt{3}}{2} ) c. ( frac{1}{sqrt{2}} ) D. ( frac{1}{sqrt{3}} ) | 11 |

359 | The ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) passes through the point (-3,1) and has the eccentricity ( sqrt{frac{2}{5}} . ) Then the major axis of the ellipse has the length: ( ^{A} cdot 4 sqrt{frac{2}{5}} ) B. ( 8 sqrt{frac{2}{3}} ) ( ^{c} cdot 4 sqrt{frac{2}{3}} ) D. ( 8 sqrt{frac{2}{5}} ) | 11 |

360 | The equation of directrix and latus rectum of a parabola are ( 3 x-4 y+ ) ( 27=0 ) and ( 3 x-4 y+2=0 . ) Then the length of latus rectum is ( mathbf{A} cdot mathbf{5} ) B . 10 c. 15 D. 20 | 11 |

361 | Length of the latus rectum of the parabola ( sqrt{boldsymbol{x}}+sqrt{boldsymbol{y}}=sqrt{boldsymbol{a}} ) is begin{tabular}{l} A ( cdot a sqrt{2} ) \ hline end{tabular} B. ( frac{a}{sqrt{2}} ) ( c ) D. 2a | 11 |

362 | Equation of the ellipse in its standard form is ( frac{boldsymbol{x}^{2}}{boldsymbol{a}^{2}}-frac{boldsymbol{y}^{2}}{boldsymbol{b}^{2}}=mathbf{1} ) A. True B. False c. Nither D. Either | 11 |

363 | (1 ) Ро 17. Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals (20015) (a) PO.RS (b) (PQ+RS)/2 (C) 2PQ.RS/(PQ+RS) (d) PO2 + RS2)/2 o | 11 |

364 | 2. A is a point on the parabola y2 = 4ax. The normal at A cuts the parabola again at point B. If AB subtends a right angle at the vertex of the parabola. find the slope of AB. (1982-5 Marks) | 11 |

365 | DU DULULU PO 20. If P and Q are the points of then there is a circle passing throu the points of intersection of the circles y + 3x + 7y + 2p-5= 0 and x2 + y2 + 2x +2y-p2=0 circle passing through P, Q and (1, 1) for: [2009] (a) all except one value of p (b) all except two values of p (C) exactly one value of p (d) all values of p The cirol. 2 21. | 11 |

366 | 25. The slope of the line touching both the parabolas y2 = 4x and x2 = -32y is [JEE M 2014] | 11 |

367 | An ellipse intersects the hyperbola 2×2 – 2y2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (2009) (a) equation of ellipse is x2 + 2y2 = 2 (b) the foci of ellipse are (-1,0) (C) equation of ellipse is x2 + 2y2 = 4 (d) the foci of ellipse are(V2,0) | 11 |

368 | Find the coordinates of the focus, equation of the directrix and the latus rectum of ( 2 x^{2}+3 y=0 ) | 11 |

369 | Find the vertex focus, equation of directrix and equation of axis of the ( boldsymbol{y}^{2}-boldsymbol{x}+mathbf{4} boldsymbol{y}+mathbf{5}=mathbf{0} ) | 11 |

370 | P2P 4 Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 277 on y-axis is (are) (JEE Adv. 2013) (a) x2 + y2 – 6x + 8y+9=0 (b) x2 + y2 – 6x + 7y+9=0 (c) x2 + y2 – 6x – 8y+9=0 (d) x2 + y2 – 6x – 7y+9=0 | 11 |

371 | U 35<m<85 The two circles x2 + y = ax each other if (a) lal=0 (c) Ja=2c (d) -85 0) touch [2011] (b) a=20 (d) 2a =C ha 41 | 11 |

372 | 11. If the circles x2 + y2 + 2ax + cy + a = 0 and for x2 + y2 – 3 ax + dy-1=0 intersect in two distinct points P and Q then the line 5x + by – a=0 passes through P and Q [2005] (a) exactly one value of a (b) no value of a (c) infinitely many values of a (d) exactly two values of a maunhan the circle with | 11 |

373 | If the eccentricity of the ellipse ( a x^{2}+ ) ( 4 y^{2}=4 a,(a<4) ) is ( frac{1}{sqrt{2}}, ) then its semi minor axis is equal to A .2 B. ( sqrt{2} ) c. 1 D. ( sqrt{3} ) E . 3 | 11 |

374 | 40. Ifthe line y=mx + 7.3 is normal to the hyperbol 24 18 = 1, then a value of m is : JEE M 2019-9 April (M) yperbola | 11 |

375 | If a 20 and the line 2bx + 3cy +4d = 0 passes th the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then [2004] (a) d2 + (36 – 2c)2 = 0 (b) d2 + (3b +2c)2 = 0 () d? +(26 – 3c)2 = 0 (d) d? +(26+ 3c)2 = 0 | 11 |

376 | The foci of a hyperbola coincide with the foci of the ellipse ( frac{x^{2}}{25}+frac{y^{2}}{9}=1 . ) Then the equation hyperbola with eccentricity 2 is A ( frac{x^{2}}{12}-frac{y^{2}}{4}=1 ) B. ( frac{x^{2}}{4}-frac{y^{2}}{12}=1 ) c. ( 3 x^{2}-y^{2}+12=0 ) D. ( 9 x^{2}-25 y^{2}-225=0 ) | 11 |

377 | Define Eccentricity? | 11 |

378 | The point (3,4) is the focus and ( 2 x- ) ( 3 y+5=0 ) is the directrix of a parabola Its latus rectum is A ( cdot frac{2}{sqrt{13}} ) в. ( frac{4}{sqrt{13}} ) c. ( frac{1}{sqrt{13}} ) D. ( frac{3}{sqrt{13}} ) | 11 |

379 | If a hyperbola passes through the foci of the ellipse ( frac{x^{2}}{25}+frac{y^{2}}{16}=1 ) and its traverse and conjugate axis coincide with major and minor axes of the ellipse, and product of the eccentricities is 1, then: This question has multiple correct options A eqaations of the hyperbola is ( frac{x^{2}}{9}-frac{y^{2}}{16}=1 ) B – Equations of the hyperbola is ( frac{x^{2}}{9}-frac{y^{2}}{25}=1 ) C. Focus of the hyperbola is (5,0) D. Focus of the hyperbola is ( (5 sqrt{3}, 0) ) | 11 |

380 | Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ. (1994 – 4 Marks) | 11 |

381 | – POOD (2011) 12. Let L be a normal to the parabola y2 = 4x. If LP El passes througe the point (9,6), then L is given by (a) y-x+3=0 (c) y + x-15 = 0 (d) y-2x + 12 = 0 (b) y + 3x – 33 = 0 | 11 |

382 | A circle passes through the point (2,1) and the line ( x+2 y=1 ) is a tangent to it at the point (3,-1) Determine its equation. | 11 |

383 | 6. The radius of the circle passing through the foci of the ellipse -= 1, and having its centre at (0,3) is lo x 22 (1995S) (a) 4 (b) 3 © 2 | 11 |

384 | vertices of an ellipse are (0,±10) and its eccentricity ( e=4 / 5 ) then its equation is A ( cdot 90 x^{2}-40 y^{2}=3600 ) B . ( 80 x^{2}+50 y^{2}=4000 ) c. ( 36 x^{2}+100 y^{2}=3600 ) D. ( 100 x^{2}+36 y^{2}=3600 ) | 11 |

385 | What does the equation ( frac{x^{2}}{r-1}- ) ( frac{y^{2}}{1+r}=1, r>1, ) represents | 11 |

386 | The eccentricity of the conic represented by ( sqrt{(x+2)^{2}+y^{2}}+ ) ( sqrt{(x-2)^{2}+y^{2}}=8 ) is A ( cdot frac{1}{3} ) в. ( frac{1}{2} ) ( c cdot frac{1}{4} ) D. | 11 |

387 | If the eccentricity of the hyperbola ( x^{2}- ) ( y^{2} sec ^{2} alpha=5 ) is ( sqrt{3} ) times the eccentricity of the ellipse ( boldsymbol{x}^{2} mathbf{s e c}^{2} boldsymbol{alpha}+ ) ( boldsymbol{y}^{2}=25, ) then the value of ( boldsymbol{alpha} ) is ( mathbf{A} cdot pi / 6 ) в. ( pi / 4 ) c. ( pi / 3 ) D. ( pi / 2 ) | 11 |

388 | The equation ( 2 x^{2}+3 y^{2}-8 x-18 y+ ) ( mathbf{3 5}=boldsymbol{lambda} ) represents? A . A circle for all ( lambda ) B. An ellipse if ( lambda0 ) D. A-point if ( lambda=0 ) | 11 |

389 | 10. the line y = x at a point P such that ere O is the origin. The circle contains the A circle touches the line y = x at a pou OP = 472 , where O is the origin. The circle point (- 10, 2) in its interior and the length of its chord on the line x + y = 0 is 62. Determine the equation of the circle. (1990 – 5 Marks) | 11 |

390 | 27. The re 27. The number of common tan sualgul le Palallel l y un number of common tangents to the circles x4 + y2 – 6x – 12=0 and x2 + y2 +6x +18y+26=0, is : [JEE M 2015) (a) 3 (6) 4 (0) 1 (d) 2 into the circles x2 + y2-4; | 11 |

391 | Find the radius and centre of the circle ( x^{2}+y^{2}-24 y+128=0 ) | 11 |

392 | For hyperbola ( frac{x^{2}}{cos ^{2} a}-frac{y^{2}}{sin ^{2} a}=1 ) which of the following remains constant with change in ‘a’? A. Abscissae of vertices B. Abscissae of foci c. Eccentricity D. Directrix | 11 |

393 | Let ( a, b ) be non-zero real numbers. The equation ( left(a x^{2}+b y^{2}+cright)left(x^{2}-5 x y+6 y^{2}right) ) represents A. four straight lines, when ( c=0 ) and ( a, b ) are of the same ( operatorname{sign} ) B. two straight lines and a circle, when ( a=b ) and ( c ) is of sign opposite to that of ( a ) C. two straight lines and a hyperbola, when ( a ) and ( b ) are of the same sign and ( c ) is of sign opposite to that of ( a ) D. a circle and an ellipse, when ( a ) and ( b ) are of the same ( operatorname{sign} ) | 11 |

394 | 8. A variable circle passes through the fixed point A(p,q) and touches x-axis. The locus of the other end of the diameter through A is [2004] (a) (y-q)2 = 4 px (b) (x – 9)2 = 4 py (c) (y-p)2 = 4qx (d) (x − p)2 = 4qy | 11 |

395 | Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola ( 16 x^{2}- ) ( 9 y^{2}=576 ) | 11 |

396 | If latus rectum of ellipse ( frac{x^{2}}{25}+frac{y^{2}}{16}=1 ) is double ordiante passing through focus of parabola ( boldsymbol{y}^{2}=mathbf{4} boldsymbol{a} boldsymbol{x}, ) then find the value of ( a ). | 11 |

397 | An ellipse passing through origin has its foci at (5,12) and ( (24,7), ) then its eccentricity is A ( cdot frac{sqrt{386}}{38} ) B. ( frac{sqrt{386}}{39} ) c. ( frac{sqrt{386}}{47} ) D. ( frac{sqrt{386}}{51} ) | 11 |

398 | If ( e_{1} ) and ( e_{2} ) are the eccentricities of two conics with ( e_{1}^{2}+e_{2}^{2}=3, ) then the conics are A. Ellipses B. Parabolas c. circles D. Hyperbolas | 11 |

399 | Find the coordinates of focus, the equation of the directrix and length of the latus rectum of the conic represented by the equation ( x^{2}=-y ) | 11 |

400 | The equations of the common tangents to the parabola y=x2 and y=-(x – 2)2 is/are (2006 – 5M, -1) (a) y=4 (x-1) (b) y=0 (c) y=4(x – 1) (d) y=-30x – 50 | 11 |

401 | 15. Find the intervals of values um um Pum). e intervals of values of a for which the line y+x=0 bisects two chords drawn from a point — (1+V2a 1-2a 32 to the circle 2x² + 2y2 – (1+V2a)x -(1-V2a)y=0). (100 ml | 11 |

402 | ( A ) and ( B ) are fixed points. If ( |P A-P B| ) is a constant, locus of ( boldsymbol{P} ) is A. a parabola B. an ellipse c. a hyperbola D. a circle | 11 |

403 | 1. A square is inscribed in the circle x2 + y2 – 2x + 4y+3=0. Its sides are parallel to the coordinate axes. The one vertex of the square is (1980) (a) (1+ V2,-2) (b) (1– V2,-2) (C) (1, -2+ 2) (d) none of these | 11 |

404 | In a parabola, length of the latus rectum is 4a. A . True B. False | 11 |

405 | Normal of the parabola ( x^{2}=8 y ) at (2,1) is A. ( 2 x+y+5=0 ) в. ( 2 x+y=5 ) ( mathbf{c} cdot 2 x-y+5=0 ) D. ( 2 x-y-5=0 ) | 11 |

406 | Find the equation of the ellipse whose vertices are ( (pm mathbf{7}, mathbf{0}) ) and foci are ( (pm mathbf{6}, mathbf{0}) ) | 11 |

407 | 38. Three circles of radii a, b, co I radii a, b, c (a <b< c) touch each other ley have x-axis as a common tangent, then: JJEEM 2019-9 Jan ( MI (c) (d) do Jo Jo a, b, c are in A.P Vā, Vī, Vc are in A.P. | 11 |

408 | 8. An ellipse has OB as semi minor axis, F and Fits focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is [2005] | 11 |

409 | Find the equation of the ellipse whose vertices are (±8,0) and foci are ( (pm mathbf{3}, mathbf{0}) ) | 11 |

410 | 18. C, and C, are two concentric circles, the radius of C, being twice that of C. From a point P on C,, tangents PA and PB are drawn to C. Prove that the centroid of the triangle PAB (1998 -8 Marks) lies on C, | 11 |

411 | The ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) cuts ( x ) axis at A and y axis at ( mathrm{B} ) and the line joining the focus ( mathrm{S} ) and ( mathrm{B} ) makes an angle ( frac{3 pi}{4} ) with x-axis. Then the eccentricity of the ellipse is A. ( frac{1}{sqrt{2}} ) в. ( frac{1}{2} ) c. ( frac{sqrt{3}}{2} ) D. ( frac{1}{3} ) | 11 |

412 | 13. If two distinct chords, drawn from the point (p, q) on the circle x2 + y2 = px + qy (where pq 0) are bisected by the x-axis, then (1999 – 2 Marks) (a) p2 = 22 (b) p2 = 892 (c) P2 8q2. | 11 |

413 | Find the equation of directrix and length of latus rectum of the parabola ( x^{2}=16 y ) A. ( y-4=0 ) and 16 B. ( y+4=0 ) and 16 c. ( y-4=0 ) and 4 D. ( y+4=0 ) and 4 | 11 |

414 | Find the area bounded by the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) and the ordinates ( x=0 ) and ( x=a e, ) where ( b^{2}=a^{2}left(1-e^{2}right) ) and ( e<1 ) | 11 |

415 | +2 a 12. For the Hyperbola – -=1, which of the cos’ a sind a following remains constant when a varies = ? (2007) (a) abscissae of vertices (b) abscissae of foci (c) eccentricity (d) directrix. | 11 |

416 | If the curve ( y=|x-3| ) touches the parabola ( boldsymbol{y}^{2}=boldsymbol{lambda}(boldsymbol{x}-mathbf{4}), boldsymbol{lambda}>mathbf{0}, ) then latus rectum of the parabola, is ( A cdot 2 ) B. 4 ( c cdot 8 ) ( D cdot 16 ) | 11 |

417 | 68. Find the coordinates of the cen- tre of the circle passing through the points (0, 0), (-2, 1) and (-3, 21. (3) (11,3) (4) (3, 11) | 11 |

418 | 11. Angle between the tanger =x2 – 5x + 6 te between the tangents to the curve y = x [2006] at the points (2,0) and (3,0) is (a) T (b) () (d) | 11 |

419 | The area of the region bounded by the curve ( sqrt{boldsymbol{x}}+sqrt{boldsymbol{y}}=sqrt{boldsymbol{a}}(boldsymbol{x}, boldsymbol{y} geq 0) ) and the coordinate axes is A ( cdot a^{2} / 6 ) в. ( a^{2} / 2 ) c. ( a^{2} / 3 ) D. ( a^{2} ) | 11 |

420 | The equation ( frac{x^{2}}{2-r}+frac{y^{2}}{r-5}+1=0 ) represents an ellipse, if ( mathbf{A} cdot r>2 ) В. ( 2<r5 ) D. ( r in(2,5) ) | 11 |

421 | Find the coordinates of focus, the equation of the directrix and length of the latus rectum of the conic represented by the equation ( 3 x^{2}=-y ) | 11 |

422 | Find the equation to the ellipse, whose focus is the point ( (-1,1), ) whose directrix is the straight line ( boldsymbol{x}-boldsymbol{y}+ ) ( mathbf{3}=mathbf{0}, ) and whose eccentricity is ( frac{mathbf{1}}{mathbf{2}} ) | 11 |

423 | If the distance of one of the focus of hyperbola from the two directrices of hyperbola are 5 and ( 3, ) then its eccentricity is A ( cdot sqrt{2} ) B. 2 ( c cdot 4 ) D. | 11 |

424 | Eccentricity of the hyperbola whose asymptotes are given by ( 3 x+2 y+ ) ( mathbf{5}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{5}=mathbf{0} ) is A ( cdot sqrt{2} ) B. ( frac{3}{2} ) ( c cdot 2 ) D. None of these | 11 |

425 | An ellipse passes through the point (4,-1) and touches the line ( x+4 y- ) ( 10=0 . ) Find its equation if its axes coincide with the coordinate axes. | 11 |

426 | On the parabola ( y=x^{2}, ) the point least distant from the straight line ( y=2 x- ) 4 is ( mathbf{A} cdot(1,1) ) B ( cdot(1,0) ) c. (1,-1) D ( cdot(0,0) ) | 11 |

427 | If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to A ( cdot frac{1}{3} ) B. ( frac{1}{sqrt{3}} ) c. ( frac{1}{sqrt{2}} ) D. ( frac{2 sqrt{2}}{3} ) E ( frac{2}{3 sqrt{2}} ) | 11 |

428 | Find the vertex, axis, focus, directrix,lastusrectum of the parabola. ( x^{2}-2 x+4 y+9=0 ) | 11 |

429 | Let circles ( C_{1} ) and ( C_{2} ) an Argand plane be given by ( |z+1|=3 ) and ( |z-2|=7 ) respectively. If a variable circle ( left|z-z_{0}right|=r quad ) be inside circle ( C_{2} ) such that it touches ( C_{1} ) externally and ( C_{2} ) internally then locus of ( z_{0} ) describes a conic ( boldsymbol{E} ) whose eccentricity is equal to A ( cdot frac{1}{10} ) B. ( frac{3}{10} ) c. ( frac{5}{10} ) D. ( frac{7}{10} ) | 11 |

430 | Find the area of a quadrant of a circle whose circumference is ( 44 mathrm{cm} ) | 11 |

431 | The eccentricity of the hyperbola whose latus-return is 8 and length of the conjugate axis is equal to half the distance between the foci, is A ( cdot frac{4}{3} ) B. ( frac{4}{sqrt{3}} ) c. ( frac{2}{sqrt{3}} ) D. None of these | 11 |

432 | Axis of a parabola is ( y=x ) and vertex and focus are at a distance ( sqrt{2} ) and ( 2 sqrt{2} ) respectively from the origin. The equation of the parabola is A ( cdot(x-y)^{2}=8(x+y-2) ) B . ( (x+y)^{2}=2(x+y-2) ) c. ( (x-y)^{2}=4(x+y-2) ) D. ( (x+y)^{2}=2(x-y+2) ) | 11 |

433 | The Vertex of the parabola ( boldsymbol{y}^{2}-mathbf{1 0} boldsymbol{y}+ ) ( boldsymbol{x}+mathbf{2 2}=mathbf{0} ) is. ( A cdot(3,4) ) B. (3,5) ( c cdot(5,3) ) D. none of these | 11 |

434 | Ratio of the greatest and least focal distances of a point on the ellipse ( 4 x^{2}+9 y^{2}=36 ) is: A. ( 4+sqrt{5}: 4-sqrt{5} ) B. ( 5+sqrt{5}: 4-sqrt{3} ) c. ( 3+sqrt{5}: 3-sqrt{5} ) D. ( sqrt{7}: 2 ) | 11 |

435 | Length of the latusrectum of the hyperbola ( boldsymbol{x} boldsymbol{y}-boldsymbol{3} boldsymbol{x}-boldsymbol{4} boldsymbol{y}+boldsymbol{8}=boldsymbol{0} ) is A .4 B. ( 4 sqrt{2} ) ( c cdot 8 ) D. None of these | 11 |

436 | Let A be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0. Suppose that the tangents at the points B(1,7) and D(4.-2) on the circle meet at the point C. Find the area of the quadrilateral ABCD. (1981 – 4 Marks) | 11 |

437 | Consider the conic ( e x^{2}+pi y^{2}-2 e^{2} x- ) ( 2 pi^{2} y+e^{3}+pi^{3}=pi e . ) Suppose ( P ) is any point on the conic and ( S_{1}, S_{2} ) are the foci of the conic, then the maximum value of ( left(boldsymbol{P S}_{1}+boldsymbol{P S}_{2}right) ) is A ( . pi e ) в. ( sqrt{pi e} ) ( c cdot 2 sqrt{pi} ) D. ( 2 sqrt{e} ) | 11 |

438 | fe is the eccentricity of the ellipse ( frac{x^{2}}{16}+frac{y^{2}}{25}=1 ) and ( e_{2} ) is the eccentricity of the hyperbola passing through the foci of the ellipse and ( e_{1} e_{2}=1, ) then equation of the hyperbola is ( stackrel{mathbf{A}}{*} frac{x^{2}}{9}-frac{y^{2}}{16}=1 ) в. ( frac{x^{2}}{16}-frac{y^{2}}{9}=-1 ) c. ( frac{x^{2}}{9}-frac{y^{2}}{25}=1 ) D. ( frac{x^{2}}{25}-frac{y^{2}}{9}=1 ) | 11 |

439 | Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse ( frac{x^{2}}{25}+frac{y^{2}}{100}=1 ) | 11 |

440 | In the ellipse distance between the foci is equal to the distance between a focus and one end of minor axis then its eccentricity is A ( cdot frac{1}{2} ) B. ( c cdot frac{1}{3} ) D. | 11 |

441 | 2. Let A be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0. Suppose that the tangents at the points B(1,7) and D(4.-2) on the circle meet at the point C. Find the area of the quadrilateral ABCD. (1981 – 4 Marks) | 11 |

442 | The co-ordinates of the focus of parabola ( boldsymbol{y}^{2}=mathbf{2 0} boldsymbol{x} ) are A. (5,5) (年) 5,5,5 B. (3,5) c. (0,5) (年. (0,5) D. (5,0) | 11 |

443 | The locus of the mid-point of a chord of the circle x + y2 = 4 which subtends a right angle at the origin 15 as a right angle at the origin is (1984 – 2 Marks) (a) x+y=2 (b) x2 + y2 = 1 (c) x² + y2=2 (d) x+y=1 | 11 |

444 | A straight line and a point not lying on it are given on a plane. Find the set of points which are equidistant from the given straight line and the given point. | 11 |

445 | The equation ( 7 y^{2}-9 x^{2}+54 x-28 y- ) ( 116=0 ) represents A. a hyperbola B. a parabola c. an ellipse D. a pair of straight lines | 11 |

446 | If the tangent to the curve, ( y=x^{3}+ ) ( a x-b ) at the point (1,-5) is perpendicular to the line, ( -boldsymbol{x}+boldsymbol{y}+ ) ( 4=0, ) then which one of the following points lies on the curve? A. (-2,2) ) в. (2,-2) c. (2,-1) D. (-2,1) | 11 |

447 | Consider the hyperbola center N(X2,0). Suppose point P(x,y) with x; er the hyperbola H:r2 – 12 = 1 and a circle S with 2,0). Suppose that Hand S touch each other at a Hand Sat 1:1) with r, >I and y, >0. The common tangent to and Sat Pintersects the x-axis at point M. If(L, m) is the roid of the triangle PMN, then the correct expression(s) (JEE Adv. 2015 is(are) (a) Pop-1-bank for x; >1 dm (d) dvi – 1 for x > 0 TL | 11 |

448 | بح 13. Tangents are drawn to the hyperbola = 1, parallel to the straight line 2x – y = 1. The points of conta tangents on the hyperbola are • The points of contact of the (2012) (C) (313,- 2/2) (d) (-313,212) | 11 |

449 | The curve represented by ( boldsymbol{R} boldsymbol{s}left(frac{1}{z}right)=boldsymbol{C} ) is (where ( C ) is a constant and ( neq 0 ) ) A. Ellipse B. Parabola c. circle D. Straight line | 11 |

450 | 23. The circle passing through the point (-1,0) and touching the y-axis at (0, 2) also passes through the point. (2011) @ (0)6 (2) © C a (-4,0) 1.defontent | 11 |

451 | 72 Pola 19. For hyperbola – -=1 which of the following cos- a sin a remains constant with change in ‘a’ (2003) (a) abscissae of vertices (b) abscissae of foci (c) eccentricity (d) directrix | 11 |

452 | If the ( operatorname{lines} 3 x-4 y-7=0 ) and ( 2 x- ) ( 3 y-5=0 ) are two diameters of a circle of area 154 square units, the equation of the circle is : A. ( x^{2}+y^{2}+2 x-2 y-62=0 ) B . ( x^{2}+y^{2}-2 x+2 y-62=0 ) c. ( x^{2}+y^{2}-2 x+2 y-47=0 ) D. ( x^{2}+y^{2}+2 x-2 y-47=0 ) | 11 |

453 | 20. If tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is (2004S) (b 2x | 11 |

454 | Trace the following central conics. ( boldsymbol{x} boldsymbol{y}=boldsymbol{a}(boldsymbol{x}+boldsymbol{y}) ) | 11 |

455 | Find the Lactus Rectum of ( 9 y^{2}- ) ( 4 x^{2}=36 ) ( mathbf{A} cdot mathbf{9} ) B. 6 c. 11 D. 15 | 11 |

456 | 19. Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,1) and has eccentricity v (a) 5×2 + 3y2 – 48=0 (c) 5x² +37² – 32=0 [2011] (b) 3×2 + 5y2 –15=0 (d) 3x² +577 – 32=0 | 11 |

457 | The length of latus rectum of the ellipse ( 4 x^{2}+9 y^{2}=36 ) is A ( cdot frac{4}{3} ) B. ( frac{8}{3} ) ( c .6 ) D. 12 | 11 |

458 | U2C ( U2UU The length of the diameter of the circle which to x-axis at the point (1,0) and passes through the p [2012] TV | 11 |

459 | 3. Find the equations of the circle passing through (4,3) and touching the lines x+y= 2 and x – y = 2. (1982 – 3 Marks) 1.. . | 11 |

460 | Assume that water issuing from the end of a horizontal pipe, 7.5 m above the ground, describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position ( 2.5 mathrm{m} ) below the line of the pipe, the flow of water has curved outward from ( 3 mathrm{m} ), beyond the vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground? | 11 |

461 | The equation ( frac{x^{2}}{10-lambda}+frac{y^{2}}{6-lambda}=1 ) represents This question has multiple correct options A. a hyperbola if ( lambda6 ) c. a hyperbola if ( 6<lambda<10 ) D. an ellipse if ( 0<lambda<6 ) | 11 |

462 | The equation of the ellipse having vertices at (±5,0) and foci (±4,0) is ( ^{A} cdot frac{x^{2}}{25}+frac{y^{2}}{16}=1 ) B. ( 9 x^{2}+25 y^{2}=225 ) c. ( frac{x^{2}}{9}+frac{y^{2}}{25}=1 ) D. ( 4 x^{2}+5 y^{2}=20 ) | 11 |

463 | Find the equation to the conic passing through the origin and the points ( (1,1),(-1,1),(2,0), ) and (3,-2) Determine its species. | 11 |

464 | In what ratio, the point of intersection of the common tangents to hyperbola ( frac{x^{2}}{1}-frac{y^{2}}{8}=1 ) and parabola ( y^{2}=12 x ) divides the foci of the given hyperbola? A . 3: 4 B. 3: 2 ( c .5: 4 ) D. 5: 3 | 11 |

465 | Trace the following central conics. ( boldsymbol{x}^{2}+boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}+boldsymbol{x}+boldsymbol{y}+mathbf{1}=mathbf{0} ) | 11 |

466 | The D on of family of circles with radius ( =5 & ) and center on ( y=2 ) is | 11 |

467 | Center of the hyperbola ( x^{2}+ ) ( 4 y^{2}+6 x y+8 x-2 y+7=0 quad ) is A ( .(1,1) ) в. (0,2) ( c cdot(2,0) ) D. None of these | 11 |

468 | Find the eccentricity, foci and the length of the latus-rectum of the ellipse ( x^{2}+ ) ( 4 y^{2}+8 y-2 x+1=0 ) | 11 |

469 | The eccentricity of the ellipse ( 12 x^{2}+ ) ( 7 y^{2}=84 ) is equal to: A ( frac{sqrt{5}}{7} ) B. ( sqrt{frac{5}{7}} ) c. ( frac{sqrt{5}}{12} ) D. E. ( frac{7}{12} ) | 11 |

470 | If one of the diameters of the circle, given by the equation, x2 + y2 – 4x + 6y-12=0, is a chord of a circle S, whose centre is at (3, 2), then the radius of Sis: JJEEM 2016] (a) 5 (b) 10 (c) 512 (d) 513 | 11 |

471 | 3. Three normals are drawn from the point (c, 0) to the curve y=x. Show that c must be greater than 1/2. One normal is always the x-axis. Find c for which the other two normals are perpendicular to each other. (1991 – 4 Marks) T . 11_D1 | 11 |

472 | Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for ( y^{2} ) ( =-8 x ) | 11 |

473 | Assertion The equation ( 3 x^{2}-2 y^{2}+4 x-6 y=0 ) represents a hyperbola. Reason The second degree equation ( a x^{2}+ ) ( 2 h x y+b y^{2}+2 g x+2 f y+c=0 ) represents a hyperbola if ( a b c+2 f g h- ) ( boldsymbol{a} boldsymbol{f}^{2}-boldsymbol{b} boldsymbol{g}^{2}-boldsymbol{c h}^{2} neq boldsymbol{0} & boldsymbol{h}^{2}>boldsymbol{a b} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 11 |

474 | If the line ( x-1=0 ) is the directrix of the parabola ( y^{2}-k x+8=0, ) then one of the values of ( k ) is A ( .1 / 8 ) B. 8 ( c cdot 4 ) D. ( 1 / 4 ) | 11 |

475 | 22. Tangents drawn from the point P(1,8) to the circle x2 + y2-6x-4-11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is (2009) (a) x2 + y2 + 4x-6y +19=0 (b) x2 + y2 – 4x – 10y +19=0 (C) x2 + y2 – 2x + 6y – 29=0 (d) x2 + y2 – 6x – 4y +19=0 | 11 |

476 | Let’d be the perpendicular distance from the centre of the ellipse Pse +2 72 62 -=1 to the tangent drawn at a point P on a² the ellipse. If F, and Fy are the two foci of the ellipse, then 62) show that (PF (1995 – 5 Marks) | 11 |

477 | In an ellipse the length of major axis is 10 and the distance between the foci is 8. Then the length of minor axis is: A . 5 B. 7 ( c cdot 4 ) D. 6 | 11 |

478 | 30. 49-12=U The eccentricity of the hyperbola whose leng rectum is equal to 8 and the length of its con equal to half of the distance between its foci, erbola whose length of the latus the length of its conjugate axis is [JEE M 2016] 4 | 11 |

479 | The curve ( 5 x^{2}+12 x y-22 x-12 y- ) ( mathbf{1 9}=mathbf{0} ) is. A . Ellipse B. Parabola c. Hyperbola D. Parallel straight lines | 11 |

480 | Find the equation of the circle with centre (-1,-2) and radius 5 | 11 |

481 | The equation of the circumcircle of the triangle formed by the lines ( y+sqrt{3} x= ) ( mathbf{6}, boldsymbol{y}-sqrt{mathbf{3}} boldsymbol{x}=mathbf{6} ) and ( boldsymbol{y}=mathbf{0} ) is A ( cdot x^{2}+y^{2}+4 x=0 ) В. ( x^{2}+y^{2}-4 y=0 ) c. ( x^{2}+y^{2}-4 y=12 ) D. ( x^{2}+y^{2}+4 x=12 ) | 11 |

482 | TO Tf2x -y+1=0 is a tangent to the hyperbola – the hyperbola 22 161, then which of the following cannot be sides of a right angled triangle? (JEE Adv. 2017) (a) a, 4,1 (b) a, 4,2 (c) 2a, 8, 1 (d) 2a, 4,1 | 11 |

483 | The eccentricity of an ellipse, with its centre a ellipse, with its centre at the origin, is If one of the directrices is x = I the directrices is x = 4, then the equation of the ellipse is: [2004] (a) 4x² +3y2 = 1 (b) 3×2 + 4y2 = 12 ©) 4x² +3y2 = 12 (d) 3×2 + 4y2 = 1 | 11 |

484 | Prove that the locus of the point of intersection of the lines ( x cos alpha+y sin alpha=a ) and ( x sin alpha-y cos alpha=b ) is a circle whatever ( alpha ) may be. | 11 |

485 | Fo parabola ( 3 y^{2}=16 x, ) equation of directrix and length of latus rectum is A ( cdot x=frac{-4}{3}, frac{3}{4} ) B. ( x=frac{4}{3}, frac{4}{3} ) c. ( y=frac{-4}{3}, frac{4}{3} ) D. ( x=frac{-4}{3}, frac{16}{3} ) | 11 |

486 | 10. One of the diameters of the circle circumscribing the rectangle ABCD is 4y = x+7. If A and B are the points (-3, 4) and (5, 4) respectively, then find the area of rectangle. (1985 – 3 Marks) | 11 |

487 | Find the equation of the hyperbola satisfying the give conditions: Foci (0,±13) the conjugate axis is of length ( mathbf{2 4} ) | 11 |

488 | Find the equation of the ellipse whose foci are (0,±7) and length of the minor axis is 26 | 11 |

489 | A focus of an ellipse is at the origin. The directrix is the line ( mathbf{x}=mathbf{4} ) and the eccentricity is ( frac{1}{2} . ) Then the length of the semi major axis is A ( cdot frac{5}{3} ) B. ( frac{8}{3} ) ( c cdot frac{2}{3} ) D. ( frac{4}{3} ) | 11 |

490 | Form the differential equation representing the family of ellipses having centre at the origin and foci on ( x ) axis. | 11 |

491 | The eccentricity of the conic ( r^{2} cos 2 theta=a^{2} ) is ( mathbf{A} cdot mathbf{1} ) B. ( sqrt{2} ) ( c cdot 2 ) D. | 11 |

492 | The foci of an ellipse are ( S(-2,-3), S^{prime}(0,1) ) and its ( e=frac{1}{sqrt{2}} ) then the directrix corresponding to the focus ( S^{prime} ) is: A. ( x+2 y-5=0 ) B . ( x+2 y-9=0 ) c. ( x+2 y-11=0 ) D. none of these | 11 |

493 | to the chord y = mx + 1 of the circle x-+y+=1 subtends an angle of measure 45° at the major segment of the circle then value of mis [2002] (a) 2012 (b) -2 (C) -1972 none of these | 11 |

494 | 33. Let (x, y) be any point on the parabola y< =4x. Let P be the point that divides the line segment from (0,0) to (x, y) in the ratio 1: 3. Then the locus of Pis (2011) (a) x2=y (b) y2 = 2x (c) y2 = x (d) x2 = 2y | 11 |

495 | Find the equation of the hyperbola satisfying the given conditions: Foci ( (pm 3 sqrt{5}, 0) ) the latus rectum is of length 8 | 11 |

496 | If foci are points (0,1)(0,-1) and minor axis is of length ( 1, ) then equation of ellipse is A ( cdot frac{x^{2}}{1 / 4}+frac{y^{2}}{5 / 4}=1 ) В. ( frac{x^{2}}{5 / 4}+frac{y^{2}}{1 / 4}=1 ) c. ( frac{x^{2}}{3 / 4}+frac{y^{2}}{1 / 4}=1 ) D. ( frac{x^{2}}{1 / 4}+frac{y^{2}}{3 / 4}=1 ) | 11 |

497 | JV 2 If a tangent to the circle x2 + y2 = lintersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is: (JEEM 2019-9 April (M)] (a) x2 + y2 – 4x2y2=0 (b) x2 + y2– 2xy=0 (©) x2 + y2 – 16xży2=0 (d) x2 + y2– 2x2y2=0 | 11 |

498 | The focus of the parabola ( boldsymbol{y}^{2}-boldsymbol{x}- ) ( 2 y+2=0 ) is ( ^{mathrm{A}} cdotleft(frac{1}{4}, 0right) ) в. (1,2) c. ( left(frac{5}{4}, 1right) ) D. ( left(frac{3}{4}, frac{5}{2}right) ) | 11 |

499 | At some point ( mathbf{P} ) on the ellipse, the segment ( mathbf{S S}^{1} ) subtends a right angle, then its eccentricity is ( ^{A} cdot_{e}=frac{sqrt{2}}{2} ) в. ( efrac{1}{sqrt{2}} ) D. ( frac{sqrt{3}}{2} ) | 11 |

500 | Equation ( (2+lambda) x^{2}-2 lambda x y+(lambda- ) 1) ( y^{2}-4 x-2=0 ) represents a hyperbola if A ( . lambda=4 ) B . ( lambda=1 ) ( c cdot lambda=frac{4}{3} ) ( D cdot lambda=3 ) | 11 |

501 | 32. The radius of a circle, having minimum area, which touches the curve y=4 – x2 and the lines, y= |x|is: (JEEM 2018] (a) 4(+2+1) (b) 2(V2 +1) (c) 2(√2-1) (d) 41/2-1). | 11 |

502 | If the latus rectum of an ellipse is equal to half of minor axis, find its eccentricity. | 11 |

503 | The line ( (x-2) cos theta+(y-2) sin theta= ) 1 touches a circle for all value of ( theta ), then the equation of circle is A ( cdot x^{2}+y^{2}-4 x-4 y+7=0 ) B . ( x^{2}+y^{2}+4 x+4 y+7=0 ) c. ( x^{2}+y^{2}-4 x-4 y-7=0 ) D. None of the above | 11 |

504 | Assertion(A): The difference of the focal distances of any point on the hyperbola ( frac{boldsymbol{x}^{2}}{mathbf{3 6}}-frac{boldsymbol{y}^{2}}{mathbf{9}}=mathbf{1} ) is 12 Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis A. Both A and R are true and R is the correct explanation of ( A ) B. Both A and R are true but R is not the correct explanation of ( A ) C. A is true but R is false. D. A is false but R is true. | 11 |

505 | The equation ( x^{2}+9=2 y^{2} ) is an example of which of the following curves? A. hyperbola B. circle c. ellipse D. parabola E. line | 11 |

506 | Find the coordinates of the focus, equation of the directrix and the latus rectum of ( boldsymbol{x}^{2}=-2 boldsymbol{y} ) | 11 |

507 | The equation ( frac{x^{2}}{2-a}+frac{y^{2}}{a-5}+1=0 ) represents an ellipse if ( boldsymbol{a} in ) ( ^{mathbf{A}} cdotleft(2, frac{3}{2}right) cupleft(frac{3}{2}, 5right) ) в. ( left(2, frac{3}{2}right) ) c. ( left(1, frac{3}{2}right) ) D. ( left(frac{3}{2}, 5right) ) | 11 |

508 | Let ( C ) be the circle with centre at (1,1) and radius ( =1 . ) If ( T ) is the circle centered at ( (0, y), ) passing through origin and touching the circle ( C ) externally, then the radius of ( T ) is equal to : A ( cdot frac{sqrt{3}}{sqrt{2}} ) B. ( frac{sqrt{3}}{2} ) ( c cdot frac{1}{2} ) D. | 11 |

509 | Find the locus of a point which moves so that the difference of its distances from the points, (5,0) and (-5,0) is 2 is: A ( cdot frac{x^{2}}{1}+frac{y^{2}}{24}=1 ) B. ( frac{x^{2}}{24}+frac{y^{2}}{1}=1 ) c. ( frac{x^{2}}{24}-frac{y^{2}}{2}=1 ) D. ( frac{x^{2}}{1}-frac{y^{2}}{24}=1 ) | 11 |

510 | Assertion ( (A): ) The eccentricity of an ellipse is ( frac{mathbf{3}}{mathbf{5}} ) Reason ( (boldsymbol{R}): ) The equation of the ellipse is ( x=5 cos theta, y=4 sin theta ) A. Assertion and reason both are correct and reason is an explanation. B. Assertion and reason both are correct and reason is not an explanation c. Assertion is incorrect and reason is correct D. Assertion is correct and reason is incorrect | 11 |

511 | 13. The equation of the directrix of the parabola y2 + 4y + 4x + 2 =0 is (a) x=-1 (b) x=1 (c) x=-3/2 (d) (20015) x=3/2 for which | 11 |

512 | Find the equation of tangents to the hyperbola ( 3 x^{2}-4 y^{2}=12, ) which make equal intercepts on the axes. | 11 |

513 | Arrange the eccentricities of the following ellipses in particular order. A- Ellipse whose Latus rectum is half of its major axis. B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis C- Ellipse whose major axis is double the minor axis. D- Ellipse whose distance between the foci is 6 and the length of minor axis is 8 ( A ) [ (A)=(C)>(D)>(B) ] B. ( (A)=(C)<(D)(C)>(D)>(B) ] D. none of these | 11 |

514 | From the following information, find the equation of Hyperbola and the equation of its Transverse Axis: Focus ( :(-2,1), ) Directrix ( : 2 x-3 y+ ) ( mathbf{1}, boldsymbol{e}=frac{mathbf{2}}{sqrt{mathbf{3}}} ) | 11 |

515 | 21. An ellipse is drawn by taking a diameter of the circle (x-1)- + y2 = 1 as its semi-minor axis and a diameter of the circle x +(y-2)2 =4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is: [2012] (a) 4×2 + y2 =4 (b) x2 + 4y2 = 8 (c) 4×2 + y2 = 8 (d) x2 + 4y2 = 16 e 1 | 11 |

516 | Find the locus of the point of intersection of the lines ( sqrt{3} x-y- ) ( 4 sqrt{3} lambda=0 ) and ( sqrt{3} lambda x+lambda y-4 sqrt{3}=0 ) for different values of ( lambda ) A ( cdot 4 x^{2}-y^{2}=48 ) B . ( x^{2}-4 y^{2}=48 ) c. ( 3 x^{2}-y^{2}=48 ) D. ( y^{2}-3 x^{2}=48 ) | 11 |

517 | The ends of major axis of an ellipse are (5,0)(-5,0) and one of the foci lies on ( 3 x-5 y-9=0, ) then the eccentricity of the ellipse is A ( cdot frac{2}{3} ) B. ( frac{3}{5} ) ( c cdot frac{4}{5} ) D. | 11 |

518 | The equation of the hyperbola whose foci are the foci of the ellipse ( frac{x^{2}}{25}+ ) ( frac{boldsymbol{y}^{2}}{mathbf{9}}=1 ) and the eccentricity is ( mathbf{2}, ) is | 11 |

519 | 3. The centre of the circle passing through the point (O touching the curve y = x2 at (2.4) is (1983 – 1 Mark) ssing through the point (0, 1) and -16 (6) (-16 53) (d) none of these | 11 |

520 | The circles ( boldsymbol{x}^{2}+boldsymbol{y}^{2}-boldsymbol{4} boldsymbol{x}+boldsymbol{4} boldsymbol{y}+boldsymbol{4}=mathbf{0} ) and ( x^{2}+y^{2}-4 x-4 y=0 ) A. Do not intersect B. Are not orthogonal c. Intersect orthogonally D. concentric | 11 |

521 | 18. If the tangent at the point Pon the circle x + y + 6x+6y=2 meets a straight line 5x-2y+6=0 at a point Q on the y-axis, then the length of PQ is (2002) (a) 4 (6) 2/5 () 5 (d) 3/5 | 11 |

522 | If the equation ( (10 x-5)^{2}+(10 y- ) 4)( ^{2}=lambda^{2}(3 x+4 y-1)^{2} ) represents a hyperbola, then : A ( .-2<lambda2 ) c. ( lambda2 ) | 11 |

523 | 35. The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is (JEE Adv. 2014) (a) 3 (b) 6 40 (c) 9 (d) 15 | 11 |

524 | Find the equation of the ellipse whose foci are (0,±3) and length of the minor axis is 16 | 11 |

525 | 20. If one of the diameters of the circle x2 + y2 – 2x – 6y+6=0 is a chord to the circle with centre (2, 1), then the radius of the circle is (2004S) a) v3 (b) VI (C) 3 (d) 2 | 11 |

526 | 9. If | m;, -i,m.>0.1=1. 2. 3. 4 are four distinct points on a circle, then show that my m2m2m4 = 1 (1989 – 2 Marks) how that m m mzma = 1 | 11 |

527 | Circles are drawn on chords of the rectangular hyperbola ( boldsymbol{x} boldsymbol{y}=mathbf{4} ) parallel to the line ( y=x ) as diameters.All such circles pass through two fixed points whose coordinates are This question has multiple correct options ( mathbf{A} cdot(2,2) ) B ( cdot(2,-2) ) c. (-2,2) D. (-2,-2) | 11 |

528 | 4 A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is [2004] (a) 6) (2-4) (a) (2,4) | 11 |

529 | Find the equation of the circle of minimum radius which contains the three circles ( boldsymbol{S}_{1} equiv boldsymbol{x}^{2}+boldsymbol{y}^{2}-boldsymbol{4} boldsymbol{y}-boldsymbol{5}=boldsymbol{0} ) ( boldsymbol{S}_{2} equiv boldsymbol{x}^{2}+boldsymbol{y}^{2}+mathbf{1 2} boldsymbol{x}+boldsymbol{4} boldsymbol{y}+boldsymbol{3 1}=mathbf{0} ) and ( S_{2} equiv x^{2}+y^{2}+6 x+12 y+ ) ( mathbf{3 6}=mathbf{0} ) | 11 |

530 | Find the area bounded by the ellipse ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1 ) and the ordinates ( x=0 ) and ( x=a e, ) where ( b^{2}=a^{2}left(1-e^{2}right) ) and ( e<1 ) | 11 |

531 | The equation of the circle passing through (4,5) having the centre at (2,2) is A ( cdot x^{2}+y^{2}+4 x+4 y-5=0 ) B . ( x^{2}+y^{2}-4 x-4 y-5=0 ) c. ( x^{2}+y^{2}-4 x=13 ) D. ( x^{2}+y^{2}-4 x-4 y+5=0 ) | 11 |

532 | 11. Two circles, each of radius 5 units, touch each other at ( the equation of their common tangent is 4x +3y=10, find the equation of the circles. (1991 – 4 Marks) | 11 |

533 | The hyperbola ( frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1 ) passes through the point ( (sqrt{6}, 3) ) and the length of the latusrectum is ( frac{18}{5} . ) Then, the length of the transverse axis is equal to A . 5 B. 4 ( c cdot 3 ) D. 2 E . 1 | 11 |

534 | Arrange the ellipses in ascending order of their eccentricities when ( angle S B S^{1} ) is given, where ( S & S^{1} ) are foci and ( B ) is one end of the minor axis. For the four ellipses ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C}, boldsymbol{D} angle mathbf{S B S}^{1}= ) ( mathbf{2 0}^{mathbf{0}}, mathbf{6 0}^{mathbf{0}}, mathbf{3 0}^{mathbf{0}}, mathbf{9 0}^{mathbf{0}} ) ( A cdot A, C, B, D ) B. D, B, C, A c. ( B, D, C, A ) D. ( A, C, D, B ) | 11 |

535 | The radius of the circle ( x^{2}+y^{2}-5 x+ ) ( 2 y+5=0 ) is ( A cdot 2 ) B. ( c cdot frac{3}{2} ) D. ( frac{2}{3} ) | 11 |

536 | Length of the latus rectum of the hyperbola ( boldsymbol{x} boldsymbol{y}-boldsymbol{3} boldsymbol{x}-boldsymbol{4} boldsymbol{y}+boldsymbol{8}=mathbf{0} ) A .4 B. ( 4 sqrt{2} ) c. 8 D. none of these | 11 |

537 | If the equation ( frac{lambda(x+1)^{2}}{3}+ ) ( frac{(y+2)^{2}}{4}=1 ) represents a circle then ( lambda= ) ( mathbf{A} cdot mathbf{1} ) в. ( frac{3}{4} ) c. 0 D. ( -frac{3}{4} ) | 11 |

538 | Find the equation of circle touching the line 2x + 3y +1=0 at (1, -1) and cutting orthogonally the circle having line segment joining (0, 3) and (-2,-1) as diameter. am | 11 |

539 | For parabola ( boldsymbol{y}^{2}=mathbf{8 4} boldsymbol{x}, ) focal distance of point (21,1764) is A . 64 B. 84 ( c cdot 24 ) D. 42 | 11 |

540 | 24. The locus of the foot of perpendicular drawn from the centre of the ellipse x2 + 3y2 = 6 on any tangent to it is (JEE M 2014] (a) (x2 + y2 )° = 6x² +2y2 (b) (x2 + y2) * = 6×2 – 2y? (©) (x² – y2)° = 6×2 + 2y2 (d) (x2 – y2) ° = 6×2 – 2y2 | 11 |

541 | 10. Intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as a diameter is [2004] (a) x2 + y2 + x – y = 0 (b) x2 + y2 – x+y=0 (C) x² + y2 +x+y=0 (d) x2 + y2 – x – y = 0 | 11 |

542 | The triangle PQR is inscribed in the circle ( x^{2}+y^{2}=25 . ) If ( Q ) and ( R ) have coordinates ( (mathbf{3}, mathbf{4}) ) and ( (-mathbf{4}, mathbf{3}) ) respectively, then ( angle Q P R ) is equal to A ( cdot frac{pi}{2} ) в. c. D. | 11 |

543 | 30. The normal at a point P on the ellipse x2 +4y2 = 16 mesta x-axis at Q. If Mis the mid point of the line segment PO then the locus of M intersects the latus rectums of the given ellipse at the points (2009) 3 (6 (+213, + 3 ) ( [+2/3, + 4/3] | 11 |

544 | What is the area enclosed by ( |x|+ ) ( |boldsymbol{y}|=mathbf{1} ? ) ( mathbf{A} cdot mathbf{1} ) B . 2 ( c .3 ) D. 4 | 11 |

545 | Eccentricity of ellipse ( frac{x^{2}}{a^{2}+1}+frac{y^{2}}{a^{2}+2}= ) 1 is ( frac{1}{sqrt{3}} ) then length of Latus rectum is A ( cdot frac{2}{sqrt{3}} ) B. ( frac{4}{sqrt{3}} ) ( c cdot 2 sqrt{3} ) D. ( frac{sqrt{3}}{2} ) | 11 |

546 | The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is A . A straight line B. A circle c. An ellipse D. A hyperbola | 11 |

547 | Eccentricity of a hyperbola is always less than 1. A. True B. False | 11 |

548 | 6. Lines 5x+12y-10=0 and 5x-12y -40=0 touch a circle C, of diameter 6. If the centre of C, lies in the first quadrant, find the equation of the circle C, which is concentric with C, and cuts intercepts of length 8 on these lines. | 11 |

549 | If ( t ) is a parameter, then ( x= ) ( left(t+frac{1}{t}right) y=bleft(t-frac{1}{t}right) ) represents A. an ellipse B. a circle c. a pair of straight lines D. a hyperbola | 11 |

550 | From any point on the hyperbola ( frac{x^{2}}{a^{2}}- ) ( frac{y^{2}}{b^{2}}=1 ) tangents are drawn to the hyperbola ( frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=2 . ) The area cut-off by the chord of contact on the asymptotes is equal to A ( cdot frac{a b}{2} ) B. ab ( c cdot 2 a b ) ( D cdot 4 a b ) | 11 |

551 | 18. The focal chord to y2 = 16x is tangent to (x – 6) + y = 2, then the possible values of the slope of this chord, are (2003) (a) {-1,1} (b) {-2,2} (c) {-2,-1/2} (d) {2,-1/2} | 11 |

552 | – 3. If the circle x2 + y2 = aintersects the hyperbola xy = c2 in four points P(x,, y,), Q(x2,y»), R(xz,yz), S(xq, y2), then (1998 – 2 Marks) (a) x, +x,+x2+x2=0 (b) y,+y,+ y +y = 0 (c) x.x2x2x4 = c4 (d) yyyy4 = c* | 11 |

553 | Let the eccentricity of the hyperbola ( frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1 ) be reciprocal to that of the ellipse ( x^{2}+4 y^{2}=4 . ) If the hyperbola passes through a focus of the ellipse, then This question has multiple correct options A the equation of the hyperbola is ( frac{x^{2}}{3}-frac{y^{2}}{2}=1 ) B. a focus of the hyperbola is (2,0) c. the eccentricity of the hyperbola is ( sqrt{frac{5}{3}} ) D. the equation of the hyperbola is ( x^{2}-3 y^{2}=3 ) | 11 |

554 | Number of intersecting points of the ( operatorname{conic} 4 x^{2}+9 y^{2}=1 ) and ( 4 x^{2}+y^{2}=4 ) is ( mathbf{A} cdot mathbf{1} ) B. 2 ( c cdot 3 ) D. 0 (zero) | 11 |

555 | The area cut off by the parabola ( y^{2}= ) ( 4 a x ) and its latus rectum is………, if ( a=3 ) | 11 |

556 | If the two circles (x – 1)2 +(y – 3)2 = r2 and 2 1,2 – 8x + 2y + 8 = 0) intersect in two distinct point, [2003] > 2 (b) 2 <r < 8 (c) r < 2 (d) r = 2. then | 11 |

557 | The point ( P ) on the parabola ( y^{2}=4 a x ) for which IPR PQI is maximum, where R ( (-a, 0), Q(0, a), ) is A ( cdot(a, 2 a) ) в. ( (a,-2 a) ) c. ( (4 a, 4 a) ) D. ( (4 a,-4 a) ) | 11 |

558 | Points A, B and C lie on the parabola y2 = 4ax. The tangents to the parabola at A, B and C, taken in pairs, intersect at points P, Q and R. Determine the ratio of the areas of the triangles ABC and PQR. (1996 – 3 Marks) 11 | 11 |

559 | The equation of a circle with through equilateral trian (a) r2+y2=9a2 (c) x² + y2=4a² ation of a circle with origin as a centre and passing equilateral triangle whose median is of length 3a is (b) x2+y=16a2 [2002] (d) x2 + y2=a2 | 11 |

560 | A circle and a parabola intersect at four points ( left(x_{1}, y_{1}right),left(x_{2}, y_{2}right),left(x_{3}, y_{3}right) ) and ( left(x_{4}, y_{4}right) . ) Then ( y_{1}+y_{2}+y_{3}+y_{4} ) is equal to ( mathbf{A} cdot mathbf{4} ) B. 3/2 ( c cdot 2 ) D. | 11 |

561 | The foci of an ellipse are located at the points (2,4) and ( (2,-2) . ) The points (4,2) lies on the ellipse. If ( a ) and ( b ) represent the lengths of the semi-major and semi-minor axes respectively, then the value of ( (a b)^{2} ) is equal to A. ( 68+22 sqrt{10} ) В. ( 6+22 sqrt{10} ) c. ( 26+10 sqrt{10} ) | 11 |

562 | 18. Iftwo tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is [2010] (a) 2x+1=0 (b) x=-1 (c) 2x-1=0 (d) x=1 to Fanation of the line | 11 |

563 | State the following statement is True or False A parabolic arch has a height 18 meters and span 24 meters. Then the height of the arch at 8 meters from the centre of the span is equal to 10 | 11 |

564 | Find the equation of a circle of radius 5 whose centre lies on ( x- ) axis and passes through the point (2,3) | 11 |

565 | 12. sally Iwo values of a A circle touches the x-axis and also touches the circle with centre at (0,3 ) and radius 2. The locus of the centre of the circle is [2005] (a) an ellipse (b) a circle (©) a hyperbola a parabola | 11 |

566 | 22. For the circle x2 + y2 = r2, find the value of r for which the area enclosed by the tangents drawn from the point P (6,8) to the circle and the chord of contact is maximum. (2003 – 2 Marks) | 11 |

567 | The circle drawn on the minor axis as diameter passes through the foci of the ellipse ( mathbf{S}=mathbf{0}, ) then its eccentricity ( mathbf{e}= ) ( mathbf{A} cdot sin 18^{0} ) B. ( sin 30^{circ} ) c. ( cos 45^{circ} ) D. ( cos 30^{circ} ) | 11 |

568 | If the line ( l x+m y+n=0 ) touches the parabola ( boldsymbol{y}^{2}=mathbf{4} boldsymbol{a} boldsymbol{x}, ) prove that ( boldsymbol{l} boldsymbol{n}= ) ( boldsymbol{a} boldsymbol{m}^{2} ) | 11 |

569 | if the distance between the foci is equal to the length of the latus-rectum. Find the eccentricity of the ellipse. A. ( frac{sqrt{5}-1}{2} ) B. ( frac{sqrt{5}+1}{2} ) c. ( frac{sqrt{5}-1}{4} ) D. None of these | 11 |

570 | The centre of the hyperbola ( 9 x^{2}-36 x- ) ( 16 y^{2}+96 y-252=0 ) is A ( .(2,3) ) в. (-2,-3) c. (-2,3) D. none of these | 11 |

571 | The latus rectum subtends a right angle at the centre of the ellipse then its eccentricity is ( A cdot 2 sin 18^{circ} ) B. ( 2 cos 18^{circ} ) ( c cdot 2 sin 54^{circ} ) ( D cdot 2 cos 54^{circ} ) | 11 |

572 | The eccentricity of an ellipse ( 9 x^{2}+ ) ( 16 y^{2}=144 ) is A ( frac{sqrt{3}}{5} ) B. ( frac{sqrt{5}}{3} ) c. ( frac{sqrt{7}}{4} ) D. | 11 |

573 | ( S ) and ( T ) are the foci of an ellipse and ( B ) is an end of the minor axis. If ( triangle boldsymbol{S T B} ) is an equilateral triangle, the eccentricity of the ellipse is equals to: A ( cdot frac{1}{4} ) B. ( frac{1}{3} ) ( c cdot frac{1}{2} ) D. ( frac{2}{3} ) E. None of these | 11 |

574 | Find the equation of the circles passing through the point (2,8) touching the line ( 4 x-3 y-24=0 ) and ( 4 x+3 y- ) ( 42=0 ) and having ( x ) coordinate of the centre of the circle less than or equal to 8 | 11 |

575 | If the parabola ( y^{2}=4 a x ) passes through (3,2) then the length of latus rectum is A ( cdot frac{1}{3} ) B. ( frac{2}{3} ) c. 1 D. | 11 |

576 | Prove that the points (7,-9) and (11,3) lie on a circle with centre at the origin. Also its equation. | 11 |

577 | Find the range of ( c ) for which the line ( boldsymbol{y}=boldsymbol{m} boldsymbol{x}+boldsymbol{c} ) touches the parabola ( boldsymbol{y}^{2}= ) ( 8(x+2) ) | 11 |

578 | A man running round a race course note that the sum of the distances of two flag posts from him is 8 meters. The area of the path he encloses in square meters if the distance between the flag posts is 4 is: ( mathbf{A} cdot 15 pi ) в. ( 12 pi ) c. ( 18 pi ) D. ( 8 sqrt{3} pi ) | 11 |

579 | Eccentricity of hyperbola ( frac{boldsymbol{x}^{2}}{boldsymbol{k}}-frac{boldsymbol{y}^{2}}{boldsymbol{k}}=mathbf{1} ) A ( cdot sqrt{1+k} ) B. ( sqrt{1-k} ) ( c cdot sqrt{2} ) ( D cdot 2 sqrt{2} ) | 11 |

580 | If the vertex ( =(2,0) ) and the extremities of the latus rectum are (3,2) and ( (3,-2), ) then the equation of the parabola is A ( cdot y^{2}=2 x-4 ) B . ( x^{2}=4 y-8 ) c. ( y^{2}=4 x-8 ) D. None | 11 |

581 | If the focal distance of an end of the minor axis of any ellipse (referred to its axes as the axes of ( x ) and ( y ) respectively) is ( k ) and the distance between the foci is ( 2 h, ) then its equation is: A ( cdot frac{x^{2}}{k^{2}}+frac{y^{2}}{k^{2}+h^{2}}=1 ) в. ( frac{x^{2}}{k^{2}}+frac{y^{2}}{h^{2}-k^{2}}=1 ) c. ( frac{x^{2}}{k^{2}}+frac{y^{2}}{k^{2}-h^{2}}=1 ) D. ( frac{x^{2}}{k^{2}}+frac{y^{2}}{h^{2}}=1 ) | 11 |

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