Question

If the length of the major axis of the ellipse $\left(\frac{x^2}{a^2}\right)+\left(\frac{y^2}{b^2}\right)=1$ is three times the length of minor axis, its eccentricity is:

• A. $\frac{1}{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\frac{2\sqrt{2}}{3}$

Answer 1

Answer: (D)

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

Given equation of ellipse $\left(\frac{x^2}{a^2}\right)+\left(\frac{y^2}{b^2}\right)=1$

We have $2a=3\left(2b\right)\Rightarrow \frac{b}{a}=\frac{1}{3}$

Hence eccentricity of the ellipse $=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{1}{9}}=\frac{2\sqrt{2}}{3}$