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(x−2). 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?(A)→(P),(S)(A)→(Q),(T)(B)→(R)(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+t2⇒t=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(x−2), we have y1=1 and x1=−2, which also satisfy the circle. (B)→(R)

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