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

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

(b) Demonstrate the result of part (a) by showing that the tangent lines to the parabola x² - 4x - 4y + 8 = 0 at the points (-2, 5) and (3, 5/4) intersect at right angles, and that the point of intersection lies on the directrix.

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