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Question

List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II.   

List IList II (A)Tangents are drawn from the point (2,3)(P)(9,6)to the parabola y2=4x. Then point(s) ofcontact is (are)(B)From a point P on the circle x2+y2=5,(Q)(1,2)the equation of chord of contact to theparabola y2=4x is y=2(x2). Thenthe coordinates of P are(C)P(4,4), Q are points on parabola(R)(2,1)y2=4x such that area of POQ is 6sq. units where O is the vertex. Thencoordinates of Q may be(D)The common chord of circle x2+y2=5(S)(4,4)and parabola 6y=5x2+7x will passthrough point(s)(T)(2,2)

Which of the following is the only CORRECT combination?
  1. (A)(P),(S)
  2. (A)(Q),(T)
  3. (B)(R)
  4. (B)(Q),(R)


Solution

The correct option is C (B)(R)
(A)
Let the point on the parabola be (t2,2t)
The equation of the tangent is,
2ty=2(x+t2)
ty=x+t2
It passes through the point (2,3), then
3t=2+t2t=1,2
The point of contact can be (1,2) or (4,4)
(A)(Q),(S)

(B)
Let a point on the circle be P(x1,y1).
Then the chord of contact of the parabola w.r.t. P is
yy1=2(x+x1)
Comparing with y=2(x2), we have
y1=1 and x1=2,
which also satisfy the circle.
(B)(R)

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