If the normal at any point of the ellipse

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If the normal at any point

P

of the ellipse

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

, meets the major and minor axes in

G

and

H

respectively and

C

in the centre of the ellipse, then prove that

a^2(CG)^2 + b^2(CH)^2 = (a^2 - b^2)^2