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ANALYTICAL GEOMETRY ONE MARK QUESTIONS. CHOOSE THE CORRECT ANSWER 1. The axis of the parabola y 2 – 2y + 8x – 23 = 0 is (a) y = – 1 (b) x = – 3 (c) x.

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Presentation on theme: "ANALYTICAL GEOMETRY ONE MARK QUESTIONS. CHOOSE THE CORRECT ANSWER 1. The axis of the parabola y 2 – 2y + 8x – 23 = 0 is (a) y = – 1 (b) x = – 3 (c) x."— Presentation transcript:

1 ANALYTICAL GEOMETRY ONE MARK QUESTIONS

2 CHOOSE THE CORRECT ANSWER 1. The axis of the parabola y 2 – 2y + 8x – 23 = 0 is (a) y = – 1 (b) x = – 3 (c) x = 3 (d) y = 1 2. 16x 2 – 3y 2 – 32x – 12y – 44 = 0 represents (a) an ellipse (b) a circle (c) a parabola (d) a hyperbola

3 Choose the correct answer 3. The line 4x + 2y = c is a tangent to the parabola y 2 = 16x then c is (a) – 1 (b) – 2 (c) 4 (d) – 4 4. The point of intersection of the tangent at t 1 = t and t 2 = 3t to the parabola y 2 = 8x is (a) (6t 2, 8t) (b) (8t, 6t 2 ) (c) (t 2, 4t) (d) (4t, t 2 )

4 Choose the correct answer 5. The length of the latus rectum of the parabola y 2 – 4x + 4y + 8 = 0 is (a) 8 (b) 6 (c) 4 (d) 2 6. The directrix of the parabola y 2 = x + 4 is (a) x = 15/4 (b) x = – 15/4 (c) x = – 17/4 (d) x = 17/4

5 Choose the correct answer 7. The length of the latus rectum of the parabola whose vertex is (2, –3) and the directrix x = 4 is (a) 2 (b) 4 (c) 6 (d) 8 8. The focus of the parabola x 2 = 16y is (a) (4, 0) (b) (0, 4) (c) (– 4, 0) (d) (0, – 4)

6 Choose the correct answer 9. The tangent at the end of any focal chord to the parabola y 2 = 12x intersect on the line (a) x – 3 = 0(b) x + 3 = 0 (c) y + 3 = 0(d) y – 3 = 0 10. The vertex of the parabola x 2 = 8y – 1 is (a) (b) (c) (d)

7 Choose the correct answer 11. The angle between the two tangents drawn from the point (– 4, 4) to the parabola y 2 = 16x is (a) 45°(b) 30° (c) 60° (d) 90° 12. The line 2x + 6y + 9 = 0 touches the parabola y 2 = 8x at the point (a) (0, – 3) (b) (2, 4) (c) (d)

8 Choose the correct answer 13. The eccentricity of the conic 9x 2 + 5y 2 – 54x – 40y + 116 = 0 is (a) 1/3 (b) 2/3 (c) 4/9 (d) 2/  5 14. The length of the semi-major and the length of minor-axis of the ellipse (a) 26, 12 (b) 13, 24 (c) 12, 26 (d) 13, 12

9 Choose the correct answer 15. The distance between the foci of the ellipse 9x 2 + 5y 2 = 180 is (a) 4 (b) 6 (c) 8 (d) 2 16. If the length of the major and semi minor-axes of an ellipse are 8, 2 and their corresponding equations are y – 6 = 0 and x + 4 = 0 then the equations of the ellipse is (a) (b) (c) (d)

10 Choose the correct answer 17. The straight line 2x – y + c = 0 is a tangent to the ellipse 4x 2 + 8y 2 = 32 if c is (a)  2  3(b)  6 (c) 36 (d)  4 18. The sum of the distance of any point on the ellipse 4x 2 + 9y 2 = 36 from (  5, 0)( –  5, 0)is (a) 4 (b) 8 (c) 6 (d) 18

11 Choose the correct answer 19. If the normal at the end of the latus rectum of the ellipse x 2 + 3y 2 = 12 intersect the major axis at G, then CG is (a) 16/3(b) 8  2/3 (c) 4  2/3 (d) 32/3 20. The radius of the director circle of the conic 9x 2 + 16y 2 = 144 is (a)  7 (b) 4 (c) 3 (d) 5

12 Choose the correct answer 21. The locus of foot of the perpendicular from the focus to a tangent of the curve 16x 2 + 25y 2 = 400 is (a) x 2 + y 2 = 4 (b) x 2 + y 2 = 25 (c) x 2 + y 2 = 16(d) x 2 + y 2 = 9 22. The eccentricity of the hyperbola 12x 2 – 4y 2 – 24x + 48y – 127 = 0 is (a) 4 (b) 3 (c) 2 (d) 6

13 Choose the correct answer 23. The tangent at any point P on the ellipse whose center C meets the major axis at T and PN is the perpendicular to the major axis then CN.CT = (a)  6(b) 3 (c)  3(d) 6 24. If Band B’ are the ends of the major axis, F 1 and F 2 are the foci of the ellipse then the area of F 1 BF 2 B’ is (a) 16 (b) 8 (c) 16  2 (d) 32  2

14 Choose the correct answer 25. The eccentricity of the hyperbola whose latus rectum is equal to half of its conjugate axis is (a)  3/2(b) 5/3 (c)  5/2(d) 3/2 26. The directrix of the hyperbola x 2 – 4(y – 3) 2 = 16 is (a) (b) (c) (d)

15 Choose the correct answer 27. The difference between the focal distances of any point on the hyperbola is 24 and the eccentricity is 2. Then the equation of the hyperbola is (a) (b) (c) (d)

16 Choose the correct answer 28. The line 5x – 2y + 4k = 0 is tangent to the hyperbola 4x 2 – y 2 = 36 then k is (a) 4/9(b) 2/3 (c) 9/4 (d) 81/16 29. The equation of the chord of contact of tangents from (2, 1) to the hyperbola is (a) 9x – 8y – 72 = 0(b) 9x + 8y + 72 = 0 (c) 8x – 9y – 72 = 0 (d) 8x + 9y + 72 = 0

17 Choose the correct answer 30. The angle between the asymptotes to the hyperbola is (a) (b) (c) (d) 31. Length of the semi-transverse axis of the rectangular hyperbola xy = 8 is (a) 2(b) 4 (c) 16 (d) 8

18 Choose the correct answer 32. The asymptotes of the hyperbola 36y 2 – 25x 2 + 900 = 0 is (a) (b) (c) (d) 33. The asymptotes of the rectangular hyperbola xy = c 2 are (a) x = c, y = c(b) x = 0, y = c (c) x = c, y = 0 (d) x = 0, y = 0

19 Choose the correct answer 34. The product of the perpendicular drawn from the point (8, 0) on the hyperbola to its asymptotes is (a) (b) (c) (d) 35. The area of the triangle formed by the tangent at any point on the rectangular hyperbola xy = 72 and its asymptotes is (a) 36(b) 18 (c) 72 (d) 144

20 Choose the correct answer 36. P is any point on the hyperbola the ordinate at P meets the asymptotes in Q and Q’ then QP.Q’P is (a) 36(b) 6 (c) 4 (d) 2 37. The locus of the point of intersection of perpendicular tangents to the hyperbola is (a) x 2 + y 2 = 25(b) x 2 + y 2 = 4 (c) x 2 + y 2 = 3 (d) x 2 + y 2 = 7

21 Choose the correct answer 38. The eccentricity of the hyperbola with asymptotes x + 2y – 5 = 0 and 2x – y + 5 = 0 is (a) 3(b)  2 (c)  3 (d) 2 39. The co-ordinate of the vertices of the rectangular hyperbola xy = 16 are (a) (4, 4), (– 4, –4)(b) (2, 8), (–2. –8) (c) (4, 0), (–4, 0) (d) (8, 0), (–8, 0)

22 Choose the correct answer 40. The length of the latus rectum of the rectangular hyperbola xy = 32 is (a) 8  2(b) 32 (c) 8 (d) 16 41. The normal to the rectangular hyperbola xy = 9 at (6, 3/2) meets the curve again at (a) (3/8, 4)(b) (–24, –3/8) (c) (–3/8, –24) (d) (24, 3/8)

23 Choose the correct answer 42. The axis of the parabola y 2 = 4x is (a) x = 0 (b) y = 0 (c) x = 1 (d) y = 1 43. The vertex of the parabola y 2 = 4x is (a) (1, 0) (b) (0, 1) (c) (0, 0) (d) (0, – 1) 44. The focus of the parabola y 2 = 4x is (a) (0, 1) (b) (1, 1) (c) (0, 0) (d) (1, 0)

24 Choose the correct answer 45. The directrix of the parabola y 2 = 4x is (a) y = – 1 (b) x = – 1 (c) y = 1 (d) x = 1 46. The equation of the latus rectum of the parabola y 2 = 4x is (a) x = 1 (b) y = 1 (c) x = 4 (d) y = – 1 47. The length of the LR of y 2 = 4x is (a) 2 (b) 3 (c) 1 (d) 4

25 Choose the correct answer 48. The axis of the parabola x 2 = – 4y is (a) y = 1 (b) x = 0 (c) y = 0 (d) x = 1 49. The vertex of the parabola x 2 = – 4y is (a) (0, 1) (b) (0, –1) (c) (1, 0) (d) (0, 0) 50. The focus of the parabola x 2 = – 4y is (a) (0, 0) (b) (0, –1) (c) (0, 1) (d) (1, 0)

26 Choose the correct answer 51. The directrix of the parabola x 2 = – 4y is (a) x = 1 (b) x = 0 (c) y = 1 (d) y = 0 52. The equation of the latus rectum of the parabola x 2 = – 4y is (a) x = –1 (b) y = –1 (c) x = 1 (d) y = 1 53. The focus of the parabola y 2 = – 8x is (a) (0, – 2) (b) (0, 2) (c) (– 2, 0) (d) (2, 0)

27 Choose the correct answer 54. The length of the LR of x 2 = – 4y is (a) 1 (b) 2 (c) 3 (d) 4 55. The axis of the parabola y 2 = – 8x is (a) x = 0 (b) x = 2 (c) y = 2 (d) y = 0 56. The vertex of the parabola y 2 = – 8x is (a) (0, 0) (b) (2, 0) (c) (0, – 2) (d) (2, – 2)

28 Choose the correct answer 57. The focus of the parabola y 2 = – 8x is (a) (0, – 2) (b) (0, 2) (c) (– 2, 0) (d) (2, 0) 58. The directrix of the parabola y 2 = – 8x is (a) y + 2 = 0 (b) x – 2 = 0 (c) y – 2 = 0 (d) x + 2 = 0 59. The equation of the latus rectum of the parabola y 2 = – 8x is (a) y –2 = 0 (b) y + 2 = 0 (c) x – 2 = 0 (d) x + 2 = 0

29 Choose the correct answer 60. The length of the LR of y 2 = – 8x is (a) 8 (b) 6 (c) 4 (d) – 8 61. The axis of the parabola x 2 = 20y is (a) y = 5 (b) x = 5 (c) x = 0 (d) y = 0 62. The vertex of the parabola x 2 = 20y is (a) (0, 5) (b) (0, 0) (c) (5, 0) (d) (0, – 5)

30 Choose the correct answer 63. The focus of the parabola x 2 = 20y is (a) (0, 0) (b) (5, 0) (c) (0, 5) (d) (– 5, 0) 64. The equation of the directrix of the parabola x 2 = 20y is (a) y – 5 = 0 (b) x + 5 = 0 (c) x – 5 = 0 (d) y + 5 = 0 65. The equation of the latus rectum of the parabola x 2 = 20y is (a) x – 5 = 0 (b) y – 5 = 0 (c) y + 5 = 0 (d) x + 5 = 0

31 Choose the correct answer 66. The length of the latus rectum of the parabola x 2 = 20y is (a) 20 (b) 10 (c) 5 (d) 4 67. If the center of the ellipse is (2, 3) one of the foci is (3, 3) then the other focus is (a) (1, 3)(b) (– 1, 3) (c) (1, – 3)(d) (–1, –3) 68. The equation of the LR s of 25x 2 + 9y 2 = 225 are (a) y =  5 (b) x =  5 (c) y =  4 (d) x =  4

32 Choose the correct answer 69. The equation of the major and minor axes of are (a) x = 3, y = 2 (b) x = – 3, y = – 2 (c) x = 0, y = 0 (d) y = 0, x = 0 70. The length of minor and major axes of are (a) 6, 4 (b) 3, 2 (c) 4, 6 (d) 2, 3

33 Choose the correct answer 71. The equations of the major and minor axes of 4x 2 + 3y 2 = 12 are (a) x =  3, y = 2 (b) x = –  3, y = – 2 (c) x = 0, y = 0 (d) y = 0, x = 0 72. The lengths of minor and major axes of the ellipse 4x 2 + 3y 2 = 12 are (a) 4, 2  3 (b) 2,  3 (c) 2  3, 4 (d) 2, 3

34 Choose the correct answer 73. The equation of the directrices of are (a) (b) (c) (d) 74. The equation of the directrices of 25x 2 + 9y 2 = 225 are (a) (b) (c) (d)

35 Choose the correct answer 75. The equation of the latus rectum of are (a) y =  7 (b) x =  7 (c) x =  7 (d) y =  7 76. If the center of the ellipse is (4, – 2) and one of the foci is (4, 2), then the other focus is (a) (4, 6) (b) (6, – 4) (c) (4, – 6) (d) (6, 4)

36 Choose the correct answer 77. The length of the LR of is (a) (b) (c) (d) 78. The length of the LR of 25x 2 + 9y 2 = 225 is (a) (b) (c) (d)

37 Choose the correct answer 79. The eccentricity of the ellipse is (a) 1/5 (b) 3/5 (c) 2/5 (d) 4/5 80. The eccentricity of the ellipse is (a)  5/3 (b)  3/5 (c) 3/5 (d) 2/3

38 Choose the correct answer 81. The eccentricity of the ellipse 16x 2 + 25y 2 = 400 is (a) 4/5 (b) 3/5 (c) ¾ (d) 2/5 82. Center of the ellipse is (a) (0, 0) (b) (5, 0) (c) (3, 5) (d) (0, 5)

39 Choose the correct answer 83. The center of the ellipse is (a) (0, 3) (b) (2, 3) (c) (0, 0) (d) (3, 0) 84. The foci of the ellipse are (a) (0,  5) (b) (0,  4) (c) (  5, 0) (d) (  4, 0)

40 Choose the correct answer 85. The foci of the ellipse are (a) (  5, 0) (b) (0,   5) (c) (0,  5) (d) (  5, 0) 86. The foci of the ellipse 16x 2 + 25y 2 = 400 are (a) (  3, 0) (b) (0,  3) (c) (0,  5) (d) (  5, 0)

41 Choose the correct answer 87. The vertices of the ellipse are (a) (0,  5) (b) (0,  3) (c) (  5, 0) (d) (  3, 0) 88. The vertices of the ellipse are (a) (0,  3) (b) (  2, 0) (c) (  3, 0) (d) (0,  2)

42 Choose the correct answer 89. The vertices of the ellipse 16x 2 + 25y 2 = 400 are (a) (0,  4) (b) (  5, 0) (c) (  4, 0) (d) (0,  5) 90. The equations of transverse and conjugate axes of the hyperbola are (a) x = 2, y = 3 (b) y = 0, x = 0 (c) x = 3, y = 2 (d) x = 0, y = 0

43 Choose the correct answer 91. The equations of transverse and conjugate axes of the hyperbola 16x 2 – 9y 2 = 144 are (a) y = 0, x = 0 (b) x = 3, y = 4 (c) x = 0, y = 0 (d) y = 3, x = 4 92. The equations of transverse and conjugate axes of the hyperbola 144x 2 – 25y 2 = 3600 are (a) y = 0, x = 0 (b) x = 12, y = 5 (c) x = 0, y = 0 (d) x = 5, y = 12

44 Choose the correct answer 93. The equations of transverse and conjugate axes of the hyperbola 8y 2 – 2x 2 = 16 are (a) x = 2  2, y =  2 (b) x =  2, y = 2  2 (c) x = 0, y = 0 (d) y = 0, x = 0 94. The equations of the directrices of the hyperbola are (a) y = (b) x = (c) y = (d) x =

45 Choose the correct answer 95. The equations of the directrices of the hyperbola 16x 2 – 9y 2 = 144 are (a) x =  (b) y =  (c) x =  (d) y =  96. The equations of the latus rectum of the hyperbola are (a) y =  13(b) y =  13 (c) x =  13(d) x =   13

46 Choose the correct answer 97. The equations of the LR of the hyperbola 16x 2 – 9y 2 = 144 are (a) y =  5 (b) x =  5 (c) y =   5 (d) x =   5 98. The length of the LR of the hyperbola are (a) 4/3(b) 8/3 (c) 3/2(d) 9/4

47 Choose the correct answer 99. The eccentricity of the hyperbola are (a) 34/3(b) 5/3 (c)  34/3(d)  34/5 100. The eccentricity of the hyperbola 25x 2 – 16y 2 = 400 is (a) (0, 4)(b) (0, 5) (c) (4, 5) (d) (0, 0)

48 Choose the correct answer 101. The foci of the hyperbola are (a) (0,  34) (b) (  34, 0) (c) (0,  34) (d) (   34, 0) 102. The vertices of the hyperbola 25x 2 – 16y 2 = 400 are (a) (0,  4) (b) (  4, 0) (c) (0,  5) (d) (  5, 0)

49 Choose the correct answer 103. The equation of the tangent at (3, – 6) to the parabola y 2 = 12x is (a) x – y – 3 = 0 (b) x + y – 3 = 0 (c) x – y + 3 = 0 (d) x + y + 3 = 0 104. The equation of the tangent at (– 3, 1) to the parabola x 2 = 9y is (a) 3x – 2y – 3 = 0 (b) 2x – 3y + 3 = 0 (c) 2x + 3y + 3 = 0 (d) 3x + 2y + 3 = 0

50 Choose the correct answer 105. The equation of chord of contact of tangents from the point (– 3, 1) to the parabola y 2 = 8x is (a) 4x – y – 12 = 0 (b) 4x + y + 12 = 0 (c) 4y – x – 12 = 0 (d) 4y – x + 12 = 0 106. The equation of chord of contact of tangents from (2, 4) to the ellipse 2x 2 + 5y 2 = 20 is (a) x – 5y + 5 = 0 (b) 5x – y + 5 = 0 (c) x + 5y – 5 = 0 (d) 5x – y – 5 = 0

51 Choose the correct answer 107. The equation of chord of contact of tangents from (5, 3) to the hyperbola 4x 2 – 6y 2 = 24 is (a) 9x + 10y + 12 = 0 (b) 10x + 9y – 12 = 0 (c) 9x – 10y + 12 = 0 (d) 10x – 9y – 12 = 0 108. The combined equation of the asymptotes to the hyperbola 36x 2 – 25y 2 = 900 is (a) 25x 2 + 36y 2 = 0 (b) 36x 2 – 25y 2 = 0 (c) 36x 2 + 25y 2 = 0 (d) 25x 2 – 36y 2 = 0

52 Choose the correct answer 109. The angle between the asymptotes of the hyperbola 24x 2 – 8y 2 = 27 is (a)  /3 (b)  /3 or 2  /3 (c) 2  /3 (d) – 2  /3 110. The point of contact of the tangent y = mx + c and the parabola y 2 = 4ax is (a) (b) (c) (d)

53 Choose the correct answer 111. The point of contact of the tangent y = mx + c and the ellipse is (a) (b) (c) (d) 112. If t 1 and t 2 are the extremities of any focal chord of a parabola y 2 = 4ax then t 1 t 2 is (a) – 1 (b) 0 (c) 1 (d) ½

54 Choose the correct answer 113. The true statements of the following are (1) Two tangents and 3 normals can be drawn to a parabola from a point (2) Two tangents and 4 normals can be drawn to an ellipse from a point (3) Two tangents and 4 normals can be drawn to a hyperbola from a point (4) Two tangents and 4 normals can be drawn to a RH from a point (a) (1), (2), (3) and (4)(b) (1) and (2) only (c) (3) and (4) only(d) (1), (2) and (3)

55 Choose the correct answer 114. The normal at t 1 on the parabola y 2 = 4ax meets the parabola at t 2 then is (a) – t 2 (b) t 2 (c) t 1 + t 2 (d) 1/t 2

56 Choose the correct answer 115. The condition that the line lx + my + n = 0 may be a normal to the ellipse is (a) at 3 + 2alm 2 + m 2 n = 0 (b) (c) (d)

57 Choose the correct answer 116. The condition that the line lx + my + n = 0 may be a normal to the hyperbola is (a) at 3 + 2alm 2 + m 2 n = 0 (b) (c) (d)

58 Choose the correct answer 117. The condition that the line lx + my + n = 0 may be a normal to the parabola y 2 = 4ax is (a) at 3 + 2alm 2 + m 2 n = 0 (b) (c) (d)

59 Choose the correct answer 118. The chord of contact of tangents from any point on the directrix of the parabola y 2 = 4ax passes though its ------------ (a) vertex (b) focus (c) directrix (d) latus rectum 119. The chord of contact of tangents from any point on the directrix of the ellipse passes though its – (a) vertex (b) focus (c) directrix (d) latus rectum

60 Choose the correct answer 120. The chord of contact of tangents from any point on the directrix of the hyperbola passes though its ------------ (a) vertex (b) focus (c) directrix (d) latus rectum 121. The point of intersection of tangents at t 1 and t 2 to the parabola y 2 = 4ax is (a) (a(t 1 + t 2 ), at 1 t 2 ) (b) (at 1 t 2, a(t 1 + t 2 )) (c) (at 2, 2at) (d) (at 1 t 2, a(t 1 – t 2 )

61 Choose the correct answer 122. The normal at the point t 1 on the parabola y 2 = 4ax meets the parabola again at t 2 then – t 2 is (a) t 1 2 (b) 1/t 1 (c) t 1 (d) t 1 + 2/t 1 123. The locus of the foot of perpendicular from the focus on any tangents to the hyperbola is (a) x 2 + y 2 = a 2 – b 2 (b) x 2 + y 2 = a 2 (c) x 2 + y 2 = a 2 + b 2 (d) x 2 + y 2 = 0

62 Choose the correct answer 124. The locus of the point of intersection of perpendicular tangents to the parabola y 2 = 4ax is (a) latus rectum (b) directrix (c) tangent at the vertex (d) axis of the parabola 125. The locus of the foot of perpendicular from the focus on any tangents to the ellipse is (a) x 2 + y 2 = a 2 – b 2 (b) x 2 + y 2 = a 2 (c) x 2 + y 2 = a 2 + b 2 (d) x 2 + y 2 = 0

63 Choose the correct answer 126. The locus of the foot of perpendicular from the focus on any tangents to the parabola y 2 = 4ax is (a) x 2 + y 2 = a 2 – b 2 (b) x 2 + y 2 = a 2 (c) x 2 + y 2 = a 2 + b 2 (d) x = 0 127. The locus of point of intersection of perpendicular tangents to the ellipse is (a) x 2 + y 2 = a 2 – b 2 (b) x 2 + y 2 = a 2 (c) x 2 + y 2 = a 2 + b 2 (d) x 2 + y 2 = 0

64 Choose the correct answer 128. The locus of point of intersection of perpendicular tangents to the hyperbola is (a) x 2 + y 2 = a 2 – b 2 (b) x 2 + y 2 = a 2 (c) x 2 + y 2 = a 2 + b 2 (d) x 2 + y 2 = 0 129. The condition that the line lx + my + n = 0 may be a tangent to the parabola y 2 = 4ax is (a) a 2 l 2 + b 2 m 2 = n 2 (b) am 2 = ln (c) a 2 l 2 – b 2 m 2 = n 2 (d) 4c 2 lm = n 2

65 Choose the correct answer 130. The condition that the line lx + my + n = 0 may be a tangent to the ellipse is (a) a 2 l 2 + b 2 m 2 = n 2 (b) am 2 = ln (c) a 2 l 2 – b 2 m 2 = n 2 (d) 4c 2 lm = n 2 131. The condition that the line lx + my + n = 0 may be a tangent to the hyperbola is (a) a 2 l 2 + b 2 m 2 = n 2 (b) am 2 = ln (c) a 2 l 2 – b 2 m 2 = n 2 (d) 4c 2 lm = n 2

66 Choose the correct answer 132. The condition that the line lx + my + n = 0 may be a tangent to the rectangular hyperbola xy = c 2 is (a) a 2 l 2 + b 2 m 2 = n 2 (b) am 2 = ln (c) a 2 l 2 – b 2 m 2 = n 2 (d) 4c 2 lm = n 2 133. If t 1 and t 2 are extremities of any focal chord of the parabola y 2 = 4ax then t 1 t 2 is (a) 1 (b) – 1 (c) 0 (d) – 2

67 Choose the correct answer 134. The foot of a perpendicular from a focus of the hyperbola on an asymptote lies on the ------- (a) centre(b) corresponding directrix (c) vertex (d) latus rectum 135. If the normal to the RH xy = c 2 at t 1 meets the curve again at t 2 then t 1 3 t 2 = (a) 1 (b) 0 (c) – 1 (d) – 2

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