Question

In an ellipse the distance between the foci is one third of the distance between the directrices, then its $e$ is

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

Answer 1

Answer: (B)

$\frac{1}{\sqrt{3}}$

Given,

$2ae=\frac{1}{3}\frac{2a}{e}$

$e^2=\frac{1}{3}$

$e=\frac{1}{\sqrt{3}}$