Let \(P\left(a t^{2}, 2 a t\right), Q, R\left(a r^{2}, 2 a r\right)\) be three points on a parabola \(y^{2}=4 a x\). If \(P Q\) is the focal chord and \(P K, Q R\) are parallel where the co-ordinates of \(K\) is \((2 a, 0)\), then the value of \(r\) is

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Let \(P\left(a t^{2}, 2 a t\right), Q, R\left(a r^{2}, 2 a r\right)\) be three points on a parabola \(y^{2}=4 a x\). If \(P Q\) is the focal chord and \(P K, Q R\) are parallel where the co-ordinates of \(K\) is \((2 a, 0)\), then the value of \(r\) is

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kritika · Answer 1 · 2021-12-27T07:21:09+0000

Ans : (D)
Hint : Slope of QR \(=\frac{2}{r-\frac{1}{t}}\)
Slope of \(P k=\frac{2 a t}{a t^{2}-2 a}=\frac{2 t}{t^{2}-2} \Rightarrow \frac{2}{r-\frac{1}{t}}=\frac{2 t}{t^{2}-2} \Rightarrow r=\frac{t^{2}-1}{t}\)

Let \(P\left(a t^{2}, 2 a t\right), Q, R\left(a r^{2}, 2 a r\right)\) be three points on a parabola \(y^{2}=4 a x\). If \(P Q\) is the focal chord and \(P K, Q R\) are parallel where the co-ordinates of \(K\) is \((2 a, 0)\), then the value of \(r\) is

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