Question

The length of the latusrectum of an ellipse is equal to one-half of its minor axis. Then the eccentricity of the ellipse is :

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

Answer 1

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

Length of latusrectum $=\frac{2b^2}{a}$ and length of minor axis $=2b$

Given $\frac{2b^2}{a}=\frac{1}{2}\left(2b\right)$

$b=\frac{a}{2}$

$e^2=1-\frac{b^2}{a^2}=\frac{a^2-\frac{a^2}{4}}{a^2}=\frac{3}{4}$

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