**LEVEL – I **

1. The equation of the tangent at the vertex of the parabola x^{2} + 4x + 2y = 0 is

(A) x = –2

(B) x = 2

(C) y = 2

(D) y = –2.

2. BC is latus rectum of a parabola y^{2} = 4ax and A is its vertex, then minimum length of projection of BC on a tangent drawn in portion BAC is

(A) a

(B) 2√a

(C) 2a

(D) 3a

3. The coordinates of the point on the parabola y = x^{2} + 7x + 2 , which is nearest to the straight line y = 3x – 3 are

(A) (-2, -8)

(B) (1, 10)

(C) (2, 20)

(D) (-1, -4)

4. The angle between tangents drawn form the point (3 , 4) to the parabola y^{2} – 2y + 4x = 0 is

(A) tan^{-1}(8√5/7)

(B) tan^{-1}(12/√5)

(C) tan^{-1}(√5/7)

(D) none of these

5. If the line x + y – 1 = 0 touches the parabola y^{2} = kx , then the value of k is

(A) 4

(B) –4

(C) 2

(D) –2

6. If (3t_{1}^{2}-6t_{1}) represents the feet of the normals to the parabola y^{2} = 12x from (1, 2), then Σ1/t_{1} is

(A) – 5/2

(B) 3/2

(C) 6

(D) –3

7. Two parabolas y^{2} = 4a(x – λ_{1}) and x^{2} = 4a(y – λ_{2}) always touch each other (λ_{1}, λ_{2} being variable parameters). Then their point of contact lies on a

(A) straight line

(B) circle

(C) parabola

(D) hyperbola

8. The graph represented by equations x = sin^{2}t , y = 2 cost is

(A) hyperbola

(B) sine graph

(C) parabola

(D) straight line

9. If 2 and 3 are the length of the segments of any focal chord of a parabola y^{2} = 4ax, then value of 2a is

(A) 13/5

(B) 12/5

(C) 11/5

(D) none of these

10. If the normals drawn at the end points of a variable chord PQ of the parabola y^{2} = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

(A) x + a = 0

(B) x – 2a = 0

(C) y^{2} – 4x + 6 = 0

(D) none of these

__ANSWER:__

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