Mathematics - Ellipse Question with Solution | TestHub

Let a be the major axis and $b$, the minor axis of the ellipse, then 3 minor axis = major axis. $\Rightarrow 3b=a$ Eccentricity is given by: $\begin{array}{l}{b}^2=a^2\left(1-e^2\right)\\ \Rightarrow b^2=9b^2\left(1-e^2\right)\\ \Rightarrow \frac{1}{9}=\left(1-e^2\right)\\ \Rightarrow e^2=\frac{8}{9}\\ \Rightarrow e=\frac{2\sqrt{2}}{3}\end{array}$