Textbook Problem

Proof

(a) Prove that if any two tangent lines to a parabola intersect at right angles, then their point of intersection must lie on the directrix.

(b) Demonstrate the result of pan (a) by showing that the

tangent lines to the parabola $x^2-4x-4y+8=0$ at the

points $(-2,5)$ and $\left(3,\frac{5}{4}\right)$ intersect at right angles and that their point of intersection lies on the directrix.