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Question

Let a,r,s,t be nonzero real numbers. Let P(at2,2at),Q,R(ar2,2ar) and S(as2,2as) be distinct points on the parabola y2=4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a,0).

The value of r is

A
1t
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B
t2+1t
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C
1t
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D
t21t
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Solution

The correct option is D t21t
We know that point Q is,
=(at2,2at)

Since, QR is parallel to PK, hence there slope must be same.
2at0at22a=2ar+2atar2at2tt22=r+1tr21t2t22t=r21t2r+1tt22t=r1tr=t21t

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