Question

Find the equation to the pair of tangents that can he drawn to the parabola from the point (x₁, y₁).

Answer 1

Let (h, k) be any point on either of the tangents drawn from (x₁, y₁). The equation to the line joining (x₁, y₁) to (h, k) is

If this be a tangent it must be of the form

Hence, by multiplication,

The locus of the point (h, k) (i.e., the pair of tangents required) is therefore

It will be seen that this equation is the same as