Question

The tangent at the point ${}^{\prime }{\alpha }^{\prime }$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the auxiliary circle in two points which subtends a right angle at the center, then the eccentricity ${}^{\prime }{e}^{\prime }$ of the ellipse is given by the equation

• A. $e^2(1+{\cos }^2\alpha )=1$
• B. $e^2(co{\sec }^2\alpha -1)=1$
• C. $e^2(1+{\sin }^2\alpha )=1$
• D. $e^2(1+{\tan }^2\alpha )=1$

Answer 1

The correct option is C $e^2(1+{\sin }^2\alpha )=1$