The tangent and normal at any point of an ellipse cut its major axis in point and…

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

Problem

The tangent and normal at any point

P

of an ellipse

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

cut its major axis in point

Q

and

R

respectively. If

QR = a

prove that the eccentric angle of the point

P

is given by

e^2 \cos^2 \phi + \cos \phi - 1 = 0