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From a point P tangents are drawn to the parabola $y^{2} = 4 a x$ . If the chord of contact subtends an angle $\frac{π}{2}$ at the vertex, then the locus of P is

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$x = - 2 a$

$x = - 3 a$

$x = - 4 a$

$y^{2} = x + 4 a$

answer is C.

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Detailed Solution

Let the ends of the chord be $t_{1} and t_{2} .$

Since the chord subtends angle $\frac{π}{2}$ at the vertex $t_{1} t_{2} = - 4$

The tangents at $t_{1} and t_{2} meet at P$

$\begin{array}{ll} ∴ P (x, y) = (a t_{1} t_{2}, a (t_{1} + t_{2})) \\ ∴ x = a t_{1} t_{2} = - 4 a \end{array}$

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