Practice Zone Maths : Hyperbola

LEVEL – I
11. The equation of hyperbola whose foci are (6, 4) and (-4, 4) and eccentricity is 2 is

(A) 12(x – 1)2 – 4(y – 4)2 = 75

(B) 4(x – 1)2 – 12(y – 4)2 = 75

(C) 12(x – 4)2 – 4(y – 1)2 = 75

(D) 4(x – 4)2 – 12(y – 1)2 = 75

12. The focus of the rectangular hyperbola (x + 4) (y – 4) = 16

(A) (-4+4√2 , 4-4√2)

(B) (-4- 4√2 , 4+4√2)

(C) (-4+4√2 , 4+4√2)

(D) none of these

13. If the line y = mx + √(a2m2 -b2) touches the hyperbola at the point (a sec θ, b tan θ) , then θ is equal to

(A) sin-1(b/am)

(B) sin-1(am/b)

(C) cos-1(am/b)

(D) none of these

14. The line y = 4x + c touches the hyperbola x2 – y2 = 1 iff

(A) c = 0

(B) c = ±√15

(C) c = ±√2

(D) none of these

15. Consider the hyperbola
Area of the triangle formed by the asymptotes and the tangent drawn to it at (a, 0) is

(A) ab/2

(B) ab

(C) 2ab

(D) 4ab

16. Number of point(s) outside the hyperbola from where two perpendicular tangents can be drawn to the hyperbola is(are)

(A) 3

(B) 2

(C) 1

(D) 0

17. If e is the eccentricity of and θ be the angle between the asymptotes, then cos(θ/2) is equal to,

(A) 1/2e

(B) 1/e

(C) 1/e2

(D) none of these

18. A normal to the parabola y2 = 4ax with slope ‘m’ touches the rectangular hyperbola x2 – y2 = a2 if.

(A) m6 + 4m4 – 3m2 + 1 = 0

(B) m6 + 4m4 + 3m2 + 1 = 0

(C) m6 – 4m4 + 3m2 – 1 = 0

(D) m6 – 4m4 – 3m2 + 1 = 0

19. If the tangent and the normal to a rectangular hyperbola xy = c2 , at a point, cuts off intercepts a1, and a2 on the x-axis and b1, b2 on the y-axis, then a1a2 + b1 b2 is equal to

(A) 3

(B) 1

(C) 2

(D) none of these

20. The length of latus rectum of the hyperbola is

(A) 2a2/b

(B) 2b2/a

(C) b2/a

(D) a2/b

ANSWER:

11. A  12. C   13. A   14. B  15. B   16. D   17. B  18. B   19. D   20. A  

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