Question

The angle between a pair of tangents drawn from a point P to the parabola y² = 4ax is 45°. Show that the locus of the point P is a hyperbola.

Answer 1

Let P (α, β) be any point on the locus. Equation of pair of tangents from P (α, β) to the parabola y² = 4ax is

Thus, the required equation of the locus is (x + 3a)² - y² = 8a² which is a hyperbola.