**LEVEL – I **

1. The line ax + by + c = 0 is a normal to the ellipse if

(A)

(B)

(C)

(D) none of these

2. The centre of ellipse is

(A) (1, 1)

(B) (2, 2)

(C) (3, 3)

(D) none of these

3. If A and B are two fixed point and P is a variable point such that PA + PB = 4 , then locus of P is

(A) ellipse

(B) circle

(C) dependents upon tangents of PA and PB

(D) depends upon length of AB

4. The set of all values of a for which represents an ellipse is

(A) (10, 11)

(B) (- ∞, 10] ∪ (10, ∞)

(C) no value of a

(D) none of these

5. The distance of a point θ on the ellipse from a focus is

(A) a (1 + e cos θ)

(B) a (e + cos θ)

(C) a (1 – cos θ)

(D) a (1 + 2 e cos θ)

6. Tangents are drawn from points on circle x^{2} + y^{2} – 4x – 6y – 12 = 0 where the x coordinate is equal to y coordinate, to the ellipse

then the angle between tangents is

(A) π/3

(B) π/4

(C) π/6

(D) none of these

7. Eccentricity of ellipse (5x – 40)^{2} + (5y – 60)^{2} = (x + 2y + 17)^{2} is

(A) 1/2

(B) 1/√3

(C) 1/4

(D) 1/√5

8. If S_{1} and S_{2} are the foci of ellipse and a point A≡ (6 , 10) , then AS_{1} + AS_{2} is

(A) 6

(B) 8

(C) 10

(D) 4

9. How many tangents can be drawn from point (2, 3) to the ellipse

(A) 1

(B) 2

(C) 0

(D) none of these

10. Let P be a variable point on the ellipse with foci F_{1} and F_{2}. Then the maximum area of triangle PF_{1}F_{2} is

(A) 24 sq unit

(B) 48 sq unit

(C) 96 sq unit

(D) none of these

__ANSWER:__

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