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If the segment intercepted by the parabola $y^{2} = 4 a x$ with the line $l x + m y + n = 0$ subtends a right angle at the vertex then

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$4 a l + 4 a m + n = 0$

$4 a m + n = 0$

$4 a l + n = 0$

$a l + n = 0$

answer is A.

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Detailed Solution

Combined equation of $\overset{\leftrightarrow}{O P}$ and $\overset{\leftrightarrow}{O Q}$ is

$y^{2} + 4 a x (\frac{l x + m y}{n}) = 0; ∵ ∠ P O Q = \frac{π}{2}; 4 a l + n = 0$

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