Question

If minor-axis of ellipse subtend a right angle at its focus then find the eccentricity of ellipse

Answer 1

Let the equation of ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$
$\because \angle BS{B}^{\prime }=\frac{\pi }{2}$ and OB = OB' $\because \angle BSO=\frac{\pi }{4}$
$\Rightarrow$ $OS=OB$ $\Rightarrow$ $ae=b$
$\Rightarrow e^2=\frac{b^2}{a^2}=1-e^2\Rightarrow e=\frac{1}{\sqrt{2}}$