**LEVEL – I **

1. The equation to the hyperbola of given transverse axis 2a along x-axis and whose vertex bisects the distance between the centre and the focus is

(A)

(B)

(C)

(D)

2. Let (5 tan θ, 3 sec θ) be a point on the hyperbola for all values of θ ≠ (2n + 1)π/2 , then find the eccentricity of the hyperbola is

(A) 5/3

(B) √(5/3)

(C) √34/9

(D) 9/√13

3. If t is a non-zero parameter then the point lies on

(A) circle

(B) parabola

(C) ellipse

(D) hyperbola

4. The locus of the points of intersection of the lines √3 x – y – 4√3t and √3t x + ty – 4√3 , for different values of t is a curve of eccentricity equal to

(A) √2

(B) 2

(C) 2/√3

(D) 4√3

5. The equation of the hyperbola whose foci are (6, 5), (-4, 5) and eccentricity 5/4 is

(A)

(B)

(C)

(D) None of these

6. The eccentricity of the hyperbola whose latus-rectum is 8 and conjugate axis is equal to half the distance between the foci, is

(A) 4/3

(B) 4/√3

(C) 2/√3

(D) none of these

7. Equation of the hyperbola passing through the point (1, -1) and having asymptotes x + 2y + 3 = 0 and 3x + 4y + 5 = 0 is

(A) 3x^{2} + 10xy + 8y^{2} + 14x + 22y + 7 = 0

(B) 3x^{2} – 10xy + 8y^{2} + 14x + 22y + 7 = 0

(C) 3x^{2} – 10xy + 8y^{2} – 14x + 22y + 7 = 0

(D) None of these

8. If the foci of the hyperbola coincide, with the ellipse

then the value of b^{2} is

(A) 1

(B) 5

(C) 7

(D) 9

9. Let P(a secθ, b tanθ) and Q(a secφ, b tanφ) where θ + φ = π/2 , be two points on the hyperbola

If (h, k) is points of intersection of normals at P and Q then k is equal to

(A) (a^{2}+b^{2})/a

(B) – (a^{2}+b^{2})/a

(C) (a^{2}+b^{2})/b

(D) – (a^{2}+b^{2})/b

10. The locus of the point from which the tangent can be drawn to the different branches of the hyperbola is

(A) k^{2}/b^{2} – h^{2}/a^{2} < 0

(B) k^{2}/b^{2} – h^{2}/a^{2} = 0

(C) k^{2}/b^{2} – h^{2}/a^{2} > 0

(D) none of these

__ANSWER:__

**1. B 2. C 3. D 4. B 5. A 6. C 7. A 8. C 9. B 10. C **