Solution

If a tangent to the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ with centre $C$ cuts the major and minor axes at $P$ and $Q$ respectively. Prove that $\dfrac{a^2}{|CP|^2} + \dfrac{b^2}{|CQ|^2} = 1$.