Question

If the length of the major axis of an ellipse is three times the length of the minor axis, then its eccentricity is

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

Answer 1

Answer: (D)

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

Let equation of ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$
According to the question,
$2a=3\left(2b\right)\Rightarrow a=3b$
$\Rightarrow a^2=9b^2$
$\Rightarrow a^2=9a^2(1-e^2)$
$\Rightarrow \frac{1}{9}=1-e^2$
$\Rightarrow e^2=1-\frac{1}{9}$
$\Rightarrow e=\frac{2\sqrt{2}}{3}$.