Question

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

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

Answer 1

The correct option is C

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

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

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