Prove that the locus of mid-points of the portion of the tangents to the ellipse…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the locus of mid-points of the portion of the tangents to the ellipse

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

intercepted between the axes is

a^2 y^2 + b^2 x^2 = 4x^2 y^2