Prove that the locus of the middle points of normal chords of the ellipse is the…

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Prove that the locus of the middle points of normal chords of the ellipse

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

\text{the curve } \left( \frac{x^2}{a^2} + \frac{y^2}{b^2} \right)^2 \left( \frac{a^6}{x^2} + \frac{b^6}{y^2} \right) = (a^2 - b^2)^2