Question

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

• A. $\frac{1}{\sqrt{6}}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$

Length of latusrectum $=\frac{2b^2}{a}$
Minor axis $=2b$
According to question,
$\frac{2b^2}{a}=b$
$\Rightarrow b=\frac{a}{2}$
$\therefore$ Eccenticity, $e=\sqrt{1-\frac{b^2}{a^2}}$
$=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}$