Tangent drawn at any point on $y^{2} = 4 a x$ meets the axis of parabola at $T$ and tangent at vertex at $S$ . If $T A S G$ is a rectangle, where $A$ is the vertex, then locus of $G$ is

y^{2} = a x

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y^{2} = - a x

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y^{2} = 2 a x

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y^{2} = - 2 a x

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Solution

The correct option is B $y^{2} = - a x$

Given parabola $y^{2} = 4 a x$
Equation of tangent is $t y = x + a t^{2}$

$x = 0 \Rightarrow S \equiv (0, a t) y = 0 \Rightarrow T \equiv (- a t^{2}, 0)$
$(h, k) = (- a t^{2}, a t)$
Then the locus of $G$ is
$h = - a {(\frac{k}{a})}^{2} ∴ y^{2} = - a x$

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