Question

$TP$ & $TQ$ are tangents to the parabola, $y^2=4ax$ at $P$ & $Q.$ If the chord $PQ$ passes through the fixed point $(-a,b)$ then the locus of $T$ is

• A. $ay=2b(x+b)$
• B. $bx=2a(y-a)$
• C. $by=2a(x-a)$
• D. $ax=2b(y-b)$

Answer 1

Answer: (C)

$by=2a(x-a)$

Let $T$ be $(x_1,y_1)$
then chord of contact equation of given parabola is
$y{y}_1=2a(x+x_1)$
Since the given chord of contact passes through $(-a,b)$
$b{y}_1=2a(x_1-a)$
Hence the locus of $T$ is $by=2a(x-a)$