Question

Find the eccentricity of an ellipse, if its latus rectum be equal to one half its minor axis.

Answer 1

Length of latus rectum $=\frac{2b^2}{a}$

Given,

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

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

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

$e=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}$