# Quizzes : Hyperbola

QUIZ – I
31. Equation of the latus rectum of the hyperbola (10x – 5)2 + (10y – 2)2 = 9(3x + 4y –7)2 is

(A) y – 1/ 5 = –3/4( x- 1/ 2)

(B) x – 1/ 5 = –3/4(y – 1/ 2)

(C) y + 1/ 5 = –3/4( x + 1/ 2)

(D) x + 1/ 5 = –3/4(y+1/ 2)

Ans: (A)

32. If PN is the perpendicular drawn from a point P on xy = c2 to its asymptote, then locus of the mid-point of PN is

(A) circle

(B) parabola

(C) ellipse

(D) hyperbola

Ans: (D)

33. Asymptotes of the hyperbola xy = 4x + 3y are

(A) x = 3 , y = 4

(B) x = 4 , y = 3

(C) x = 2 , y = 6

(D) x= 6 , y = 2

Ans: (A)

34. The distance between foci of a hyperbola is 16 and its eccentricity is √2, then the equation of hyperbola is

(A) x2 – y2 = 3

(B) x2 – y2 = 16

(C) x2 – y2 = 15

(D) x2 – y2 = 32

Ans: (D)

35. The point of intersection of tangents at ‘ t1 ‘ and ‘ t2 ‘ to the hyperbola xy = c2 is

(A) $\large (\frac{c t_1 t_2}{t_1 + t_2} , \frac{c }{t_1 + t_2} )$

(B) $\large (\frac{2c t_1 t_2}{t_1 + t_2} , \frac{2c }{t_1 + t_2} )$

(C) $\large (\frac{ t_1 t_2}{c(t_1 + t_2)} , \frac{t_1 + t_2 }{c} )$

(D) none of these

Ans: (B)

36. The equation 2x2 + 3y2 – 8x – 18y + 35 = 0 represents

(A) a point

(B) parabola

(C) hyperbola

(D) ellipse

Ans: (A)

37. A circle cuts two perpendicular lines so that each intercept is of given length. The locus of the centre of the circle is a conic whose eccentricity is

(A) 1

(B) 1/√2

(C) √2

(D) none of these

Ans: (C)

38. The locus of the point of intersection of tangents at the extremities of the chords of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$  which are tangents to the circle drawn on the line joining the foci as diameter is

(A) $\frac{x^2}{a^2}-\frac{y^2}{b^2} = \frac{1}{a+b}$

(B) $\frac{x^2}{a^4}+\frac{y^2}{b^4} = \frac{1}{a^2+b^2}$

(C)  x2 + y2 = a2 + b2

(D) x2 – y2 = a2 + b2

Ans: (B)

39. If the portion of the asymptote between centre and the tangent at the vertex of hyperbola$\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$  in the third quadrant is cut by the line y + λ(x + a) = 0 ; λ being parameter, then

(A) λ ∈ R+

(B) λ ∈ R

(C) λ ∈ (0, 1)

(D) none of these

Ans: (A)

40. The equation of the common tangent to the curves y2 = 8x and xy = –1 is

(A) 3y = 9x + 2

(B) y = 2x + 1

(C) 2y = x + 8

(D) y = x + 2

Ans: (D)

41. Let S1 and S2 be the foci of a rectangular hyperbola, which has the centre at Q, then for any point P on the hyperbola S1P . S2P equals to

(A) S1 . S22

(B) QS12

(C) QP2

(D) 4QP2

Ans: (C)

42. The values of ‘m’ for which a line with slope m is common tangent to the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$ (a ≠ b) and parabola y2 = 4ax is

(A) m ∈ (0, ∞)

(B) m ∈ (-∞, -1) ∪ (1, ∞) -{±√(1+√5)/2}

(C) m ∈(-∞, 2) – √(1+√5)/2

(D) none of these

Ans: (B)

43. The chord PQ of the hyperbola xy = c2 meets the x-axis at A. If R be the mid point of PQ and O be the centre of the hyperbola, then the triangle ARO is necessarily

(A) equilateral

(B) isosceles

(C) right angled

(D) obtuse angled

Ans: (B)

44. Minimum length of a normal chord to the hyperbola xy = c2 lying between different branches is

(A) √2 c

(B) 2c

(C) 2 √2 c

(D) none of these

Ans: (C)

45. If the tangent at the point P(h , k) on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$ cuts the circle x2 + y2 = a2 at the points Q(x1, y1) and R(x2, y2), then = 1/y1 + 1/y2

(A) 2/k

(B) 1/k

(C) a/k

(D) b/k

Ans: (A)

46. The reflection of the curve xy = 1 in the line y = 2x is the curve 12x2 + r xy + sy2 + t = 0, then the value of r is

(A) – 7

(B) 25

(C) – 175

(D) none of these

Ans: (A)

47. The angle between lines joining the origin to the points of intersection of the line √3x + y = 2 and the curve y2 – x2 = 4 is equal to

(A) tan-1(2/√3)

(B) π/6

(C) tan-1(√3/2)

(D) π/2

Ans: (C)

48. The number of real points at which the line 3y – 2x = 14 cuts the hyperbola $\frac{(x-1)^2}{9}-\frac{(y-2)^2}{4} = 5$ is

(A) 2

(B) 3

(C) 4

(D) none of these

Ans: (D)

49. The line 2x + y = 0 passes through the centre of a rectangular hyperbola, one of whose asymptotes is x – y = 1. The equation of the other asymptote is

(A) 3x + 3y + 1 = 0

(B) 3x + 3y – 1 = 0

(C) x – 2y = 0

(D) none of these

Ans: (A)

50. A line y = 2x + 5 intersects a hyperbola only at a point (-2 , 1). The equation of one of its asymptotes is 3x + 2y + 1 = 0. If hyperbola passes through a point (-1 , 0), then the equation of hyperbola is

(A) 6x2 + xy – 2y2 + 35x – 21y + 29 = 0

(B) 6x2 + xy – 2y2 – 35x – 21y + 29 = 0

(C) 6x2 + xy – 2y2 + 35x – 21y – 29 = 0

(D) none of these