If $P Q$ is a normal chord of the parabola $y^{2} = 4 a x$ at $P (a t^{2}, 2 a t) .$ Then the axis of the parabola divides $¯ ¯¯¯¯¯¯ ¯ P Q$ in the ratio

\frac{t^{2}}{t^{2} + 2}

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\frac{t^{2}}{t^{2} - 2}

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\frac{2 t^{2}}{t^{2} - 2}

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\frac{t^{2}}{2 (t^{2} - 2)}

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Solution

The correct option is A $\frac{t^{2}}{t^{2} + 2}$
Let $P Q$ be normal chord, $P (a t^{2}, 2 a t), Q (a t_{2}^{2}, 2 a t_{2}), t_{2} = - t - \frac{2}{t}$
$As X-axis divides normal chord in the ratio - y_{1} : y_{2}$
$= \frac{- 2 a t}{2 a t_{2}} = \frac{t^{2}}{t^{2} + 2}$

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