Mathematics

Problem

Tangents at right angles are drawn to the ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

. Show that the locus of the middle points of the chord of contact is the curve

\left(\frac{x^2}{a^2} + \frac{y^2}{b^2}\right)^2 = \frac{x^2 + y^2}{a^2 + b^2}