Let a,r,s,t be nonzero real numbers. Let P(at2,2at),Q,R(ar2,2ar) and S – InterviewSolution

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1.	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
Answer» Let $a, r, s, t$ be nonzero real numbers. Let $P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r) and S (a s^{2}, 2 a s)$ be distinct points on the parabola $y^{2} = 4 a x$ . Suppose that $P Q$ is the focal chord and lines $Q R$ and $P K$ are parallel, where $K$ is the point $(2 a, 0) .$ The value of $r$ is

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