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 )