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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?

A
(C)(Q),(S)
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B
(C)(P),(T)
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C
(D)(P),(S)
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D
(D)(Q),(R)
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Solution

The correct option is D (D)(Q),(R)
(C)
Let Q(t2,2t) be a point on the parabola.
Now, the area of triangle OPQ is
∣ ∣ ∣ ∣12∣ ∣ ∣ ∣0044t22t00∣ ∣ ∣ ∣∣ ∣ ∣ ∣=68t+4t2=±12t2+2t+1=1±3(t+1)2=2 or 4
(t+1)2=4t=1±2t=3,1
Then, the point Q is (1,2) or (9,6).
(C)(P),(Q)

(D)
Points (1,2) and (2,1) satisfy both the curves.
(D)(Q),(R)

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