A normal inclined at an angle of to -axis of the ellipse is drawn

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

Problem

A normal inclined at an angle of

45^\circ

x

-axis of the ellipse

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

is drawn. It meets the major and minor axes in

P

and

Q

respectively. If

C

is the centre of the ellipse, prove that area of

\Delta CPQ

\frac{(a^2 - b^2)^2}{2(a^2 + b^2)}

sq units.