Question

If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is

• A. 3/2
• B.
• C. 2/3
• D.

Answer 1

The correct option is B

$\frac{2b^2}{a}=b\Rightarrow \frac{b}{a}=\frac{1}{2}\Rightarrow \frac{b^2}{a^2}=\frac{1}{4}$

Hence e = $\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{3}}{2}$ .