If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

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

Solution:

Equation of a tangent to the parabola is $y = m x + 1 / m .$ If it passes through $P (h, k)$ , then

$k = m h + 1 / m$

$\Rightarrow m^{2} h - m k + 1 = 0$ which gives the slopes of two tangents passing through P. As these are at right angles, product of the $s l o p e s = - 1 \Rightarrow 1 / h = - 1$ Locus of $P$ is $x = - 1$ which is the directrix of the parabola.

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

Solution:

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