Question

If the major axis of an ellipse is $3$ times its minor axis, then its eccentricity of the ellipse is

• A. $\frac{2}{3}$
• B. $\frac{\sqrt{2}}{3}$
• C. $\frac{2\sqrt{2}}{3}$
• D. $\frac{4\sqrt{2}}{3}$

Answer 1

Answer: (C)

$\frac{2\sqrt{2}}{3}$

The major axis of the ellipse $\left(2a\right)=3\times 2b$ (where $2b$ is the minor axis of the ellipse$)$

$\Rightarrow a=3b.$

We know that the relation for the eccentricity of an ellipse $\left(e\right),$ when $a<b,$ is $e^2=\frac{a^2-b^2}{a^2}=\frac{\left(9b^2\right)-b^2}{9b^2}=\frac{8}{9}\Rightarrow e=\frac{2\sqrt{2}}{3}.$