Mathematics - Ellipse Question with Solution | TestHub

The length of minor axis is given by $\left(2b\right)$ and the distance between foci is given by $\left(2ae\right)$

Given: $2b=\frac{1}{2}\times 2ae$

$\Rightarrow 2b=ae$

$\Rightarrow 4b^2=a^2{e}^2$

$\Rightarrow \frac{4b^2}{a^2}=e^2$

$\Rightarrow 4\left(1-e^2\right)=e^2$

$\Rightarrow 4-4e^2=e^2$

$\Rightarrow e=\frac{2}{\sqrt{5}}$