Question

Consider the parabola \(y^{2}=4 x .\) Let \(P\) and \(Q\) be points on the parabola where \(P .(4,-4) \& Q(9,6) .\) Let \(R\) be a point on the arc of the parabola between \(\mathrm{P} \& \mathrm{Q}\). Then the area of \(\triangle \mathrm{PQR}\) is largest when
(A) \(\angle \mathrm{PQR}=90^{\circ}\)
(B) \(R(4,4)\)
(C) \(\mathrm{R}\left(\frac{1}{4}, 1\right)\)
(D) \(\mathrm{R}\left(1, \frac{1}{4}\right)\)
Ans: (C)

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