Solution:
Equation of a tangent to the parabola is y = mx + 1/m. If it passes through P(h, k), then
k = mh + 1/m
⇒m2h−mk+1=0 which gives the slopes of two tangents passing through P. As these are at right angles, product of the slopes =– 1⇒ 1/h = – 1 Locus of P is x =– 1 which is the directrix of the parabola.
