Question

If the normals drawn at the end points of a variable chord $PQ$ of the parabola $y^2=4ax$ intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points $P$ and $Q$ is

• A. $x+a=0$
• B. $x-2a=0$
• C. $y^2-4x+6=0$
• D. $y^2+4x-6=0$

Answer 1

The correct option is A $x+a=0$

PQ must be a focal chord.

Tangents at ends of focal chord must be perpendicular.

Point R lie on director circle.

Therefore locus is given by $x=-a$

$\Rightarrow x+a=0$