Show that the line touches the ellipse if and that point of contact is .

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

Problem

Show that the line

x \cos \alpha + y \sin \alpha = p

touches the ellipse

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

a^2 \cos^2 \alpha + b^2 \sin^2 \alpha = p^2

and that point of contact is

\left( \frac{a^2 \cos \alpha}{p}, \frac{b^2 \sin \alpha}{p} \right)