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The length of the chord $P Q$ is.

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$5 a$

$7 a$

$3 a$

$2 a$

answer is B.

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Detailed Solution

Let $P = (a t^{2}, 2 a t)$

$Q = (\frac{a}{t^{2}}, - \frac{2 a}{t})$

and $R = (- a, a (t - \frac{1}{t}))$

Since $R$ lies on $y = 2 x + a,$ So

$\begin{array}{l} a (t - \frac{1}{t}) = - a \\ \Rightarrow (t - \frac{1}{t}) = - 1 \\ \Rightarrow {(t + \frac{1}{t})}^{2} = {(t - \frac{1}{t})}^{2} + 4 \end{array}$

$= 1 + 4$

$= 5$

Thus, $P Q = a {(t + \frac{1}{t})}^{2} = 5 a$

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