Question

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

Answer 1

if tangents drawn from point P to the parabola

${y}^{2} = 4(1)x$

are at right angles, therefore locus of P is the directrix of the parabola, i.e.

$x + 1 = 0$

which is a straight line

Answer 2

Given : parabola $y^2 = 4x$

To find : locus of p

Explanation:

since , we know that locus of point P from which two perpendiculars tangents are drawn to the parabola is the directrix of the parabola

then

the equation is

(y-k)² = 4p(x-h)  has focus (h+p,k) and its directrix is x=h-p

thus here ,

h = 0 , k=0 , p=1

directrix  is x=0-1 = -1

hence , the required equation is x  = -1

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