Transcript Document

ANALYTICAL
GEOMETRY
ONE MARK QUESTIONS
CHOOSE THE CORRECT ANSWER
1.
2.
The axis of the parabola y2 – 2y + 8x – 23 = 0 is
(a) y = – 1
(b) x = – 3
(c) x = 3
(d) y = 1
16x2 – 3y2 – 32x – 12y – 44 = 0 represents
(a) an ellipse
(b) a circle
(c) a parabola
(d) a hyperbola
Choose the correct answer
3.
The line 4x + 2y = c is a tangent to the parabola
y2 = 16x then c is
4.
(a) – 1
(b) – 2
(c) 4
(d) – 4
The point of intersection of the tangent at t1 = t
and t2 = 3t to the parabola y2 = 8x is
(a) (6t2, 8t)
(b) (8t, 6t2)
(c) (t2, 4t)
(d) (4t, t2)
Choose the correct answer
5.
The length of the latus rectum of the parabola
y2 – 4x + 4y + 8 = 0 is
6.
(a) 8
(b) 6
(c) 4
(d) 2
The directrix of the parabola y2 = x + 4 is
(a) x = 15/4
(b) x = – 15/4
(c) x = – 17/4
(d) x = 17/4
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
8.
(a) 2
(b) 4
(c) 6
(d) 8
The focus of the parabola x2 = 16y is
(a) (4, 0)
(b) (0, 4)
(c) (– 4, 0)
(d) (0, – 4)
Choose the correct answer
9.
The tangent at the end of any focal chord to the
parabola y2 = 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 x2 = 8y – 1 is
 1 
(a)   ,0 
 8 
1 
 ,0 
8 
(b)
 1
(c)  0, 
 8
1

(d)  0, 8 


Choose the correct answer
11. The angle between the two tangents drawn from
the point (– 4, 4) to the parabola y2 = 16x is
(a) 45°
(b) 30°
(c) 60°
(d) 90°
12. The line 2x + 6y + 9 = 0 touches the parabola
y2 = 8x at the point
(a) (0, – 3)
(b) (2, 4)
9

(c)   6, 
2

(d)  9 ,6 
2

Choose the correct answer
13. The eccentricity of the conic
9x2 + 5y2 – 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
x2
y2

1
minor-axis of the ellipse
144 169
(a) 26, 12
(b) 13, 24
(c) 12, 26
(d) 13, 12
Choose the correct answer
15. The distance between the foci of the ellipse
9x2 + 5y2 = 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
( x  4) 2 ( y  6) 2
(a)

1
4
16
( x  4) 2 ( y  6) 2
(b)

1
16
4
( x  4) 2 ( y  6) 2
(c) 16  4  1
( x  4) 2 ( y  6) 2

1
(d)
4
16
Choose the correct answer
17. The straight line 2x – y + c = 0 is a tangent to
the ellipse 4x2 + 8y2 = 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 4x2 + 9y2 = 36 from (5, 0)( –5, 0)is
(a) 4
(b) 8
(c) 6
(d) 18
Choose the correct answer
19. If the normal at the end of the latus rectum of
the ellipse x2 + 3y2 = 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
9x2 + 16y2 = 144 is
(a) 7
(b) 4
(c) 3
(d) 5
Choose the correct answer
21. The locus of foot of the perpendicular from
the focus to a tangent of the curve
16x2 + 25y2 = 400 is
(a) x2 + y2 = 4
(b) x2 + y2 = 25
(c) x2 + y2 = 16
(d) x2 + y2 = 9
22. The eccentricity of the hyperbola
12x2 – 4y2 – 24x + 48y – 127 = 0 is
(a) 4
(b) 3
(c) 2
(d) 6
Choose the correct answer
x2 y2
1
23. The tangent at any point P on the ellipse 
6
3
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, F1 and
F2 are the foci of the ellipse x 2 y 2
then the

1
area of F1BF2B’ is
8
4
(a) 16
(b) 8
(c) 162
(d) 322
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
x2 – 4(y – 3)2 = 16 is
8
(a) y  
5
8
(b) x  
5
5
(c) y  
8
5
(d) x  
8
Choose the correct answer
27. The difference between the focal distances of
x2 y2
any point on the hyperbola 2  2  1 is 24
a
b
and the eccentricity is 2. Then the equation of
the hyperbola is
x2
y2
(a)

1
144 432
x2
y2
(b)

1
432 144
x2
y2
(c) 12  12 3  1
x2
y2

1
(d)
12 3 12
Choose the correct answer
28. The line 5x – 2y + 4k = 0 is tangent to the
hyperbola 4x2 – y2 = 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
2
2
from (2, 1) to the hyperbola x  y  1 is
16 9
(a) 9x – 8y – 72 = 0
(b) 9x + 8y + 72 = 0
(c) 8x – 9y – 72 = 0
(d) 8x + 9y + 72 = 0
Choose the correct answer
30. The angle between the asymptotes to the
2
2
x
y
hyperbola

 1 is
16 9
(a)   2 tan  3 
4
4
(b)   2 tan  
3
3
(c) 2 tan  
4
4
(d) 2 tan  
3
1
1
1
1
31. Length of the semi-transverse axis of the
rectangular hyperbola xy = 8 is
(a) 2
(b) 4
(c) 16
(d) 8
Choose the correct answer
32. The asymptotes of the hyperbola
36y2 – 25x2 + 900 = 0 is
6
(a) y   x
5
36
(c) y   x
25
5
(b) y   x
6
25
(d) y   x
36
33. The asymptotes of the rectangular hyperbola
xy = c2 are
(a) x = c, y = c
(b) x = 0, y = c
(c) x = c, y = 0
(d) x = 0, y = 0
Choose the correct answer
34. The product of the perpendicular drawn from the
point (8, 0) on the hyperbola to its asymptotes
x2 y2
is

1
64
36
25
(a)
576
6
(c)
25
(b)
576
25
(d)
25
6
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
Choose the correct answer
36. P is any point on the hyperbola
x2 y2

1
64 36
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
2
2
x
y
perpendicular tangents to the hyperbola

1
16 9
is
(a) x2 + y2 = 25
(b) x2 + y2 = 4
(c) x2 + y2 = 3
(d) x2 + y2 = 7
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)
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)
Choose the correct answer
42. The axis of the parabola y2 = 4x is
(a) x = 0
(b) y = 0
(c) x = 1
(d) y = 1
43. The vertex of the parabola y2 = 4x is
(a) (1, 0)
(b) (0, 1)
(c) (0, 0)
(d) (0, – 1)
44. The focus of the parabola y2 = 4x is
(a) (0, 1)
(b) (1, 1)
(c) (0, 0)
(d) (1, 0)
Choose the correct answer
45. The directrix of the parabola y2 = 4x is
(a) y = – 1
(b) x = – 1
(c) y = 1
(d) x = 1
46. The equation of the latus rectum of the parabola
y2 = 4x is
(a) x = 1
(b) y = 1
(c) x = 4
(d) y = – 1
47. The length of the LR of y2 = 4x is
(a) 2
(b) 3
(c) 1
(d) 4
Choose the correct answer
48. The axis of the parabola x2 = – 4y is
(a) y = 1
(b) x = 0
(c) y = 0
(d) x = 1
49. The vertex of the parabola x2 = – 4y is
(a) (0, 1)
(b) (0, –1)
(c) (1, 0)
(d) (0, 0)
50. The focus of the parabola x2 = – 4y is
(a) (0, 0)
(b) (0, –1)
(c) (0, 1)
(d) (1, 0)
Choose the correct answer
51. The directrix of the parabola x2 = – 4y is
(a) x = 1
(c) y = 1
(b) x = 0
(d) y = 0
52. The equation of the latus rectum of the parabola
x2 = – 4y is
(a) x = –1
(c) x = 1
(b) y = –1
(d) y = 1
53. The focus of the parabola y2 = – 8x is
(a) (0, – 2)
(c) (– 2, 0)
(b) (0, 2)
(d) (2, 0)
Choose the correct answer
54. The length of the LR of x2 = – 4y is
(a) 1
(b) 2
(c) 3
(d) 4
55. The axis of the parabola y2 = – 8x is
(a) x = 0
(b) x = 2
(c) y = 2
(d) y = 0
56. The vertex of the parabola y2 = – 8x is
(a) (0, 0)
(b) (2, 0)
(c) (0, – 2)
(d) (2, – 2)
Choose the correct answer
57. The focus of the parabola y2 = – 8x is
(a) (0, – 2)
(b) (0, 2)
(c) (– 2, 0)
(d) (2, 0)
58. The directrix of the parabola y2 = – 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
y2 = – 8x is
(a) y –2 = 0
(b) y + 2 = 0
(c) x – 2 = 0
(d) x + 2 = 0
Choose the correct answer
60. The length of the LR of y2 = – 8x is
(a) 8
(b) 6
(c) 4
(d) – 8
61. The axis of the parabola x2 = 20y is
(a) y = 5
(b) x = 5
(c) x = 0
(d) y = 0
62. The vertex of the parabola x2 = 20y is
(a) (0, 5)
(b) (0, 0)
(c) (5, 0)
(d) (0, – 5)
Choose the correct answer
2
63. The focus of the parabola x = 20y is
(a) (0, 0)
(c) (0, 5)
(b) (5, 0)
(d) (– 5, 0)
64. The equation of the directrix of the parabola
x2 = 20y is
(a) y – 5 = 0
(c) x – 5 = 0
(b) x + 5 = 0
(d) y + 5 = 0
65. The equation of the latus rectum of the parabola
x2 = 20y is
(a) x – 5 = 0
(c) y + 5 = 0
(b) y – 5 = 0
(d) x + 5 = 0
Choose the correct answer
66. The length of the latus rectum of the parabola
x2 = 20y is
(a) 20
(c) 5
(b) 10
(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 25x2 + 9y2 = 225 are
(a) y =  5
(c) y =  4
(b) x =  5
(d) x =  4
Choose the correct answer
69. The equation of the major and minor axes of
x2 y2

1
9
4
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
x2 y2

1
are
9
4
(a) 6, 4
(b) 3, 2
(c) 4, 6
(d) 2, 3
Choose the correct answer
71. The equations of the major and minor axes of
4x2 + 3y2 = 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 4x2 + 3y2 = 12 are
(a) 4, 23
(b) 2, 3
(c) 23, 4
(d) 2, 3
Choose the correct answer
x2 y2

 1 are
73. The equation of the directrices of
16 9
16
(a) y   4
(b) x  
7
7
16
(c) x  
7
16
(d) y  
7
74. The equation of the directrices of
25x2 + 9y2 = 225 are
4
(a) x  
25
25
(b) x  
4
4
(c) y  
25
25
(d) y  
4
Choose the correct answer
2
2
x
y
75. The equation of the latus rectum of

1
16 9
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)
Choose the correct answer
x2 y2
77. The length of the LR of is

1
16 9
9
2
(a)
(b)
2
9
9
(c)
16
16
(d)
9
78. The length of the LR of 25x2 + 9y2 = 225 is
(a) 9
2
18
(b)
5
(c) 25
(d)
9
5
18
Choose the correct answer
x2 y2
79. The eccentricity of the ellipse

1
25 9
(a) 1/5
(b) 3/5
(c) 2/5
(d) 4/5
80. The eccentricity of the ellipse
x2 y2

1
4
9
(a) 5/3
(b) 3/5
(c) 3/5
(d) 2/3
is
is
Choose the correct answer
81. The eccentricity of the ellipse 16x2 + 25y2 = 400
is
(a) 4/5
(b) 3/5
(c) ¾
(d) 2/5
82. Center of the ellipse
x2 y2

1
25 9
(a) (0, 0)
(b) (5, 0)
(c) (3, 5)
(d) (0, 5)
is
Choose the correct answer
83. The center of the ellipse
x2 y2

1
4
9
(a) (0, 3)
(b) (2, 3)
(c) (0, 0)
(d) (3, 0)
2
2
x
y
84. The foci of the ellipse

 1 are
25 9
(a) (0,  5)
(b) (0,  4)
(c) ( 5, 0)
(d) ( 4, 0)
is
Choose the correct answer
x2 y2
85. The foci of the ellipse are

1
4
9
(a) ( 5, 0)
(b) (0,  5)
(c) (0,  5)
(d) ( 5, 0)
86. The foci of the ellipse 16x2 + 25y2 = 400 are
(a) ( 3, 0)
(b) (0,  3)
(c) (0,  5)
(d) ( 5, 0)
Choose the correct answer
87. The vertices of the ellipse
x2 y2

 1 are
25 9
(a) (0,  5)
(b) (0,  3)
(c) ( 5, 0)
(d) ( 3, 0)
x2 y2
88. The vertices of the ellipse

1
4
9
(a) (0,  3)
(b) ( 2, 0)
(c) ( 3, 0)
(d) (0,  2)
are
Choose the correct answer
89. The vertices of the ellipse 16x2 + 25y2 = 400 are
(a) (0,  4)
(b) ( 5, 0)
(c) ( 4, 0)
(d) (0,  5)
90. The equations of transverse and conjugate axes
x2 y2

 1 are
of the hyperbola
9
4
(a) x = 2, y = 3
(b) y = 0, x = 0
(c) x = 3, y = 2
(d) x = 0, y = 0
Choose the correct answer
91. The equations of transverse and conjugate axes
of the hyperbola 16x2 – 9y2 = 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 144x2 – 25y2 = 3600 are
(a) y = 0, x = 0
(b) x = 12, y = 5
(c) x = 0, y = 0
(d) x = 5, y = 12
Choose the correct answer
93. The equations of transverse and conjugate axes
of the hyperbola 8y2 – 2x2 = 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
x2 y2

1
9
4
9
(a) y = 
13
13
(c) y = 
9
are
13
(b) x = 
9
9
(d) x = 
13
Choose the correct answer
95. The equations of the directrices of the hyperbola
16x2 – 9y2 = 144 are
(a) x =  5
9
9
(c) x = 
5
9
(b) y = 
5
(d) y =  5
9
96. The equations of the latus rectum of the
x2 y2
hyperbola

 1 are
9
4
(a) y =  13
(b) y = 13
(c) x =  13
(d) x =  13
Choose the correct answer
97. The equations of the LR of the hyperbola
16x2 – 9y2 = 144 are
(a) y =  5
(b) x =  5
(c) y =  5
(d) x =  5
x2 y2
98. The length of the LR of the hyperbola

1
9
4
are
(a) 4/3
(b) 8/3
(c) 3/2
(d) 9/4
Choose the correct answer
x2 y2
99. The eccentricity of the hyperbola

1
9 25
are
(a) 34/3
(b) 5/3
(c) 34/3
(d) 34/5
100. The eccentricity of the hyperbola 25x2 – 16y2 =
400 is
(a) (0, 4)
(b) (0, 5)
(c) (4, 5)
(d) (0, 0)
Choose the correct answer
101. The foci of the hyperbola
x2 y2

1
9 25
are
(a) (0, 34)
(b) ( 34, 0)
(c) (0,  34)
(d) ( 34, 0)
102. The vertices of the hyperbola 25x2 – 16y2 = 400
are
(a) (0,  4)
(b) ( 4, 0)
(c) (0,  5)
(d) ( 5, 0)
Choose the correct answer
103.The equation of the tangent at (3, – 6) to the
parabola y2 = 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 x2 = 9y is
(a) 3x – 2y – 3 = 0
(b) 2x – 3y + 3 = 0
(c) 2x + 3y + 3 = 0
(d) 3x + 2y + 3 = 0
Choose the correct answer
105.The equation of chord of contact of tangents
from the point (– 3, 1) to the parabola y2 = 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 2x2 + 5y2 = 20 is
(a) x – 5y + 5 = 0
(b) 5x – y + 5 = 0
(c) x + 5y – 5 = 0
(d) 5x – y – 5 = 0
Choose the correct answer
107. The equation of chord of contact of tangents
from (5, 3) to the hyperbola 4x2 – 6y2 = 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 36x2 – 25y2 = 900 is
(a) 25x2 + 36y2 = 0 (b) 36x2 – 25y2 = 0
(c) 36x2 + 25y2 = 0 (d) 25x2 – 36y2 = 0
Choose the correct answer
109. The angle between the asymptotes of the
hyperbola 24x2 – 8y2 = 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 y2 = 4ax is
(a)
 a 2a 
 2, 
m m 
(b)
(c)
 a 2a 
 , 2
m m 
(d)
 2a a 
 2, 
m m
  a  2a 
 2,

m 
m
Choose the correct answer
111. The point of contact of the tangent y = mx + c
x2 y2
and the ellipse 2  2  1
a
b
2
2
b a m
(a)  c , c 


 a 2m  b2 
(c)  , 
c 
 c
is
  a 2m b2 
(b)  c , c 


  a 2m  b2 

,
(d)
c 
 c
112. If t1 and t2 are the extremities of any focal chord
of a parabola y2 = 4ax then t1t2 is
(a) – 1
(b) 0
(c) 1
(d) ½
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)
Choose the correct answer
114. The normal at t1 on the parabola y2 = 4ax meets

2

the parabola at t2 then  t1  
t1 

(a) – t2
(b) t2
(c) t1 + t2
(d) 1/t2
is
Choose the correct answer
115. The condition that the line lx + my + n = 0 may
x2 y2
be a normal to the ellipse 2  2  1
a
b
(a)
at3
+
2alm2
+
m2n
a 2 b 2 (a 2  b 2 ) 2
(c) 2  2 
l
m
n2
=0
is
2
2
2
2 2
a
b
(
a

b
)
(b) 2  2 
l
m
n2
a 2 b 2 (a 2  b 2 ) 2
(d) 2  2 
l
m
n2
Choose the correct answer
116. The condition that the line lx + my + n = 0 may
be a normal to the hyperbola
(a)
at3
+
2alm2
+
m2n
a 2 b 2 (a 2  b 2 ) 2
(c) 2  2 
l
m
n2
=0
x2 y2
 2 1
2
a
b
is
2
2
2
2 2
a
b
(
a

b
)
(b) 2  2 
l
m
n2
2
2
2
2 2
a
b
(
a

b
)
(d) 2  2 
l
m
n2
Choose the correct answer
117. The condition that the line lx + my + n = 0 may
be a normal to the parabola y2 = 4ax is
(a)
at3
+
2alm2
+
m2n
=0
a 2 b 2 (a 2  b 2 ) 2
(c) 2  2 
l
m
n2
2
2
2
2 2
a
b
(
a

b
)
(b) 2  2 
l
m
n2
2
2
2
2 2
a
b
(
a

b
)
(d) 2  2 
l
m
n2
Choose the correct answer
118. The chord of contact of tangents from any point
on the directrix of the parabola y2 = 4ax passes
though its -----------(a) vertex
(b) focus
(c) directrix
(d) latus rectum
119. The chord of contact of tangents from any point
2
2
x
y
on the directrix of the ellipse 2  2  1 passes
a
b
though its –
(a) vertex
(b) focus
(c) directrix
(d) latus rectum
Choose the correct answer
120.The chord of contact of tangents from any point
2
2
x
y
on the directrix of the hyperbola 2  2  1passes
a
b
though its -----------(a) vertex
(b) focus
(c) directrix
(d) latus rectum
121.The point of intersection of tangents at t1 and t2
to the parabola y2 = 4ax is
(a) (a(t1 + t2), at1t2)
(b) (at1t2, a(t1 + t2))
(c) (at2, 2at)
(d) (at1t2, a(t1 – t 2)
Choose the correct answer
122. The normal at the point t1 on the parabola y2 =
4ax meets the parabola again at t2 then – t2 is
(a) t12
(b) 1/t1
(c) t1
(d) t1 + 2/t1
123. The locus of the foot of perpendicular from the
2
2
x
y
focus on any tangents to the hyperbola
 2 1
2
a
b
is
(a) x2 + y2 = a2 – b2
(b) x2 + y2 = a2
(c) x2 + y2 = a2 + b2
(d) x2 + y2 = 0
Choose the correct answer
124.The locus of the point of intersection of
perpendicular tangents to the parabola y2 = 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
2
2
x
y
focus on any tangents to the ellipse 2  2  1 is
a
b
(a) x2 + y2 = a2 – b2
(b) x2 + y2 = a2
(c) x2 + y2 = a2 + b2
(d) x2 + y2 = 0
Choose the correct answer
126.The locus of the foot of perpendicular from the
focus on any tangents to the parabola y2 = 4ax is
(a) x2 + y2 = a2 – b2
(b) x2 + y2 = a2
(c) x2 + y2 = a2 + b2
(d) x = 0
127.The locus of point of intersection of
x2 y2
perpendicular tangents to the ellipse 2  2  1is
a
b
(a) x2 + y2 = a2 – b2
(b) x2 + y2 = a2
(c) x2 + y2 = a2 + b2
(d) x2 + y2 = 0
Choose the correct answer
128. The locus of point of intersection of
2
2
x
y
perpendicular tangents to the hyperbola 
1
2
2
a
b
is
(a) x2 + y2 = a2 – b2
(b) x2 + y2 = a2
(c) x2 + y2 = a2 + b2
(d) x2 + y2 = 0
129. The condition that the line lx + my + n = 0 may
be a tangent to the parabola y2 = 4ax is
(a) a2 l2 + b2 m2 = n2
(b) am2 = ln
(c) a2 l2 – b2 m2 = n2
(d) 4c2 lm = n2
Choose the correct answer
130. The condition that the line lx + my + n = 0 may
2
2
x
y
be a tangent to the ellipse 2  2  1 is
a
b
(a) a2 l2 + b2 m2 = n2
(b) am2 = ln
(c) a2 l2 – b2 m2 = n2
(d) 4c2 lm = n2
131. The condition that the line lx + my + n = 0 may
2
2
x
y
be a tangent to the hyperbola
is


1
a 2 b2
(a) a2 l2 + b2 m2 = n2
(b) am2 = ln
(c) a2 l2 – b2 m2 = n2
(d) 4c2 lm = n2
Choose the correct answer
132.The condition that the line lx + my + n = 0 may be
a tangent to the rectangular hyperbola xy = c2 is
(a) a2 l2 + b2 m2 = n2
(b) am2 = ln
(c) a2 l2 – b2 m2 = n2
(d) 4c2 lm = n2
133.If t1 and t2 are extremities of any focal chord of
the parabola y2 = 4ax then t1t2 is
(a) 1
(b) – 1
(c) 0
(d) – 2
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 = c2 at t1 meets the
curve again at t2 then t13 t2 =
(a) 1
(b) 0
(c) – 1
(d) – 2