Let and be the extremities of a chord of an ellipse

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

A(\theta)

and

B(\phi)

be the extremities of a chord of an ellipse. If the slope of

AB

is equal to the slope of the tangent at a point

C(\alpha)

on the ellipse, then the value of

\alpha

is (1)

\frac{\theta + \phi}{2}

(2)

\frac{\theta - \phi}{2}

(3)

\frac{\theta + \phi}{2} + \pi

(4)

\frac{\theta + \phi}{2} - \pi