analytical geometry one mark questions. choose the correct answer 1. the axis of the parabola y 2...

ANALYTICAL GEOMETRY

ONE MARK QUESTIONS

PREPARED BY:R.RAJENDRAN. M.A., M. Sc., M. Ed.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21

CHOOSE THE CORRECT ANSWER

1. The axis of the parabola y2 – 2y + 8x – 23 = 0 is

(a) y = – 1 (b) x = – 3

(c) x = 3 (d) y = 1

2. 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

(a) – 1 (b) – 2

(c) 4 (d) – 4

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)


5. The length of the latus rectum of the parabola

y2 – 4x + 4y + 8 = 0 is

(a) 8 (b) 6

(c) 4 (d) 2

6. 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


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 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

(a) (b)

(c) (d)

0,

8

1

0,8

1

8

1,0

8

1,0

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)

(c) (d)

6,

2

9

2

9,6

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

minor-axis of the ellipse

(a) 26, 12 (b) 13, 24

(c) 12, 26 (d) 13, 12

1169144

22

yx

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

(a) (b)

(c) (d)

116

)6(

4

)4( 22

yx

14

)6(

16

)4( 22

yx

14

)6(

16

)4( 22

yx

116

)6(

4

)4( 22

yx

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) 23 (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) 82/3

(c) 42/3 (d) 32/3

20. The radius of the director circle of the conic9x2 + 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 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, F1 and F2 are the foci of the ellipse then the area of F1BF2B’ is(a) 16 (b) 8

(c) 162 (d) 322

136

22

yx

148

22

yx

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

(a) (b)

(c) (d)

5

8y

5

8x

8

5y

8

5x


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)

12

2

2

2

b

y

a

x

1432144

22

yx

1144432

22

yx

131212

22

yx

112312

22

yx

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 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

1916

22

yx

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

1916

22

yx

4

3tan2 1

3

4tan2 1

4

3tan2 1

3

4tan2 1

Choose the correct answer 32. The asymptotes of the hyperbola

36y2 – 25x2 + 900 = 0 is

(a) (b)

(c) (d)

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

xy5

6 xy

6

5

xy25

36 xy

36

25

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

13664

22

yx

25

576

576

25

6

25

25

6

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) x2 + y2 = 25 (b) x2 + y2 = 4

(c) x2 + y2 = 3 (d) x2 + y2 = 7

13664

22

yx

1916

22

yx

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) 82 (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 answer42. 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)


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


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)


51. The directrix of the parabola x2 = – 4y is

(a) x = 1 (b) x = 0

(c) y = 1 (d) y = 0


x2 = – 4y is

(a) x = –1 (b) y = –1

(c) x = 1 (d) y = 1

53. The focus of the parabola y2 = – 8x is

(a) (0, – 2) (b) (0, 2)

(c) (– 2, 0) (d) (2, 0)


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)


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


y2 = – 8x is

(a) y –2 = 0 (b) y + 2 = 0

(c) x – 2 = 0 (d) x + 2 = 0


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 answer63. The focus of the parabola x2 = 20y is

(a) (0, 0) (b) (5, 0)

(c) (0, 5) (d) (– 5, 0)

64. The equation of the directrix of the parabola

x2 = 20y is

(a) y – 5 = 0 (b) x + 5 = 0

(c) x – 5 = 0 (d) y + 5 = 0


x2 = 20y is

(a) x – 5 = 0 (b) y – 5 = 0

(c) y + 5 = 0 (d) x + 5 = 0

Choose the correct answer66. The length of the latus rectum of the parabola

x2 = 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 25x2 + 9y2 = 225 are

(a) y = 5 (b) x = 5

(c) y = 4 (d) x = 4


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

149

22

yx

149

22

yx


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, 23 (b) 2, 3

(c) 23, 4 (d) 2, 3


73. The equation of the directrices of are

(a) (b)

(c) (d)

74. The equation of the directrices of

25x2 + 9y2 = 225 are

(a) (b)

(c) (d)

1916

22

yx

7

4y

7

16x

7

16x

7

16y

25

4x

4

25x

4

25y

25

4y


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)

1916

22

yx


77. The length of the LR of is

(a) (b)

(c) (d)

78. The length of the LR of 25x2 + 9y2 = 225 is

(a) (b)

(c) (d)

1916

22

yx

2

9

9

2

16

9

9

16

2

95

18

9

2518

5


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

1925

22

yx

194

22

yx


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 is

(a) (0, 0) (b) (5, 0)

(c) (3, 5) (d) (0, 5)

1925

22

yx


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)

194

22

yx

1925

22

yx


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 16x2 + 25y2 = 400 are

(a) ( 3, 0) (b) (0, 3)

(c) (0, 5) (d) ( 5, 0)

194

22

yx


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)

1925

22

yx

194

22

yx


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

of the hyperbola are

(a) x = 2, y = 3 (b) y = 0, x = 0

(c) x = 3, y = 2 (d) x = 0, y = 0

149

22

yx



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


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 answer93. The equations of transverse and conjugate axes

of the hyperbola 8y2 – 2x2 = 16 are

(a) x = 22, y = 2 (b) x = 2, y = 22

(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 =

149

22

yx

13

9

9

13

9

13

13

9


95. The equations of the directrices of the hyperbola

16x2 – 9y2 = 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

9

55

9

5

9

9

5

149

22

yx


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

98. The length of the LR of the hyperbola

are

(a) 4/3 (b) 8/3

(c) 3/2 (d) 9/4

149

22

yx


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 25x2 – 16y2 =

400 is

(a) (0, 4) (b) (0, 5)

(c) (4, 5) (d) (0, 0)

1259

22

yx


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 25x2 – 16y2 = 400

are

(a) (0, 4) (b) ( 4, 0)

(c) (0, 5) (d) ( 5, 0)

1259

22

yx


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


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


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


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) (b)

(c) (d)

m

a

m

a 2,

2

m

a

m

a,

22

2

2,m

a

m

a

m

a

m

a 2,

2


111. The point of contact of the tangent y = mx + c

and the ellipse is

(a) (b)

(c) (d)

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

12

2

2

2

b

y

a

x

c

ma

c

b 22

,

c

b

c

ma 22

,

c

b

c

ma 22

,

c

b

c

ma 22

,

Choose the correct answer113. 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)


114. The normal at t1 on the parabola y2 = 4ax meets

the parabola at t2 then is

(a) – t2 (b) t2

(c) t1 + t2 (d) 1/t2

11

2

tt


115. The condition that the line lx + my + n = 0 may

be a normal to the ellipse is

(a) at3 + 2alm2 + m2n = 0 (b)

(c) (d)

12

2

2

2

b

y

a

x

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a



be a normal to the hyperbola is

(a) at3 + 2alm2 + m2n = 0 (b)

(c) (d)

12

2

2

2

b

y

a

x

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a



be a normal to the parabola y2 = 4ax is

(a) at3 + 2alm2 + m2n = 0 (b)

(c) (d)

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a

2

222

2

2

2

2 )(

n

ba

m

b

l

a

Choose the correct answer118. 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

on the directrix of the ellipse passes

though its –



12

2

2

2

b

y

a

x


120.The chord of contact of tangents from any point

on the directrix of the hyperbola

passes though its ------------



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)

12

2

2

2

b

y

a

x

Choose the correct answer122. 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

focus on any tangents to the hyperbola

is

(a) x2 + y2 = a2 – b2 (b) x2 + y2 = a2

(c) x2 + y2 = a2 + b2 (d) x2 + y2 = 0

12

2

2

2

b

y

a

x


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

focus on any tangents to the ellipse is

(a) x2 + y2 = a2 – b2 (b) x2 + y2 = a2

(c) x2 + y2 = a2 + b2 (d) x2 + y2 = 0

12

2

2

2

b

y

a

x


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

perpendicular tangents to the ellipse is

(a) x2 + y2 = a2 – b2 (b) x2 + y2 = a2

(c) x2 + y2 = a2 + b2 (d) x2 + y2 = 0

12

2

2

2

b

y

a

x


128. The locus of point of intersection of

perpendicular tangents to the hyperbola

is

(a) x2 + y2 = a2 – b2 (b) x2 + y2 = a2

(c) x2 + y2 = a2 + b2 (d) x2 + y2 = 0


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

12

2

2

2

b

y

a

x



be a tangent to the ellipse is

(a) a2 l2 + b2 m2 = n2 (b) am2 = ln

(c) a2 l2 – b2 m2 = n2 (d) 4c2 lm = n2


be a tangent to the hyperbola is

(a) a2 l2 + b2 m2 = n2 (b) am2 = ln

(c) a2 l2 – b2 m2 = n2 (d) 4c2 lm = n2

12

2

2

2

b

y

a

x

12

2

2

2

b

y

a

x


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


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

analytical geometry one mark questions. choose the correct answer 1. the axis of the parabola y 2...

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