The locus of point which moves such that the tangent from which to a parabola y2 =4ax are at right angle.
Let two tangents are drawn from point P.
Given equation of parabola is: y2=4ax.............(i)
We know that the locus of point P from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola.
The standard equation of parabola (y - k)2 = 4p(x-h) has focus (x+h, k) and the directrix is (h - p).
From (i), we get,
h=0, k=0, p=1
Directrix of (i) is x= 0 - 1 = -1
Hence, the required locus is x= -1