WBJEE · Maths · Parabola
Let \(P\left(a t^{2}, 2 a t\right), Q,\) R(ar \(^{2}, 2ar)\) 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
- A \(\frac{t}{1-t^{2}}\)
- B \(\frac{1-t^{2}}{t}\)
- C \(\frac{t^{2}+1}{t}\)
- D \(\frac{t^{2}-1}{t}\)
Answer & Solution
Correct Answer
(D) \(\frac{t^{2}-1}{t}\)
Step-by-step Solution
Detailed explanation
Here, coordinate of \(Q\) will be \(\left(\frac{a}{t^{2}}, \frac{-2 a}{t}\right)\) Slope of \(Q R=\frac{2}{r-\frac{1}{t}}\) Slope of \(P K=\frac{2 a t}{a t^{2}-2 a}=\frac{2 t}{t^{2}-2}\) since, slope of \(Q R=\) slope of \(P K\)…
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