Mathematics - Ellipse Question with Solution | TestHub

$e=\cos \alpha$ eccentricity $LR=\frac{2\times {\tan }^2\alpha }{\sec \alpha }=2\left[\frac{1}{\cos \alpha }-\cos \alpha \right]$ where $0<\alpha <\frac{\pi }{4}$ Which is an increasing function $\therefore LR\in (0,\sqrt{2})$ Also $OP=O{S}_1=1$ clearly $\tan \alpha <1$ as $0<\alpha <\frac{\pi }{4}$ $\Rightarrow \mathrm{P}$ lies outside the ellipse.