M.C.Q : Parabola (1 to 10)

LEVEL – I
1. The equation of the tangent at the vertex of the parabola x2 + 4x + 2y = 0 is

(A) x = –2

(B) x = 2

(C) y = 2

(D) y = –2.

2. BC is latus rectum of a parabola y2 = 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 = x2 + 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 y2 – 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 y2 = kx , then the value of k is

(A) 4

(B) –4

(C) 2

(D) –2

6. If (3t12-6t1) represents the feet of the normals to the parabola y2 = 12x from (1, 2), then Σ1/t1 is

(A) – 5/2

(B) 3/2

(C) 6

(D) –3

7. Two parabolas y2 = 4a(x – λ1) and x2 = 4a(y – λ2) always touch each other (λ1, λ2 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 = sin2t , 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 y2 = 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 y2 = 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) y2 – 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 

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M.C.Q : Parabola ( 11 to 20 )

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