Question

If two tangents drawn from a point$P$ to the parabola $y^2=4x$ are at right angles, then the locus of$P$ is

• A. $2x+1=0$
• B. $x=-1$
• C. $2x-1=0$
• D. $x=1$

Answer 1

The correct option is B

$x=-1$

The Explanation for the correct answer.

If tangents are perpendicular to the point$P$then point$P$lies on the directrix of the parabola

Locus of$P=$ the directrix of $y^2=4x$

Equation of directrix is given by:

$x=-a=-1$

Therefore, the locus of$P$ is $x=-1$

Hence, Option (B) is the correct answer.