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TP and TQ are...

Question

$T P$ and $T Q$ are tangents to the parabola $y^{2} = 4 a x$ at points $P$ and $Q$ . If the chord $P Q$ passes through a fixed point $(- a, b)$ , then the locus of $T$ is

A

b y = 2 a (x - a)

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B

a x = 2 b (y - b)

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C

b x = 2 a (y - a)

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D

a y = 2 b (x - b)

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Solution

The correct option is A $b y = 2 a (x - a)$
Let $T \equiv (h, k)$
$P Q : K y = 2 a (x + h)$ passes through $(- a, b)$
$\Rightarrow b K = 2 a (h - a)$
$\Rightarrow b y = 2 a (x - a)$

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