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