Question

Find the eccentricity of that ellipse, whose latus rectum is half of the minor axis.

Answer 1

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

Length of minor axis $=2b$

Given:

Latus rectum $=\frac{1}{2}$(length of minor axis)

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

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

Eccentricity $e=\frac{c}{a}$ where $c=\sqrt{(a^2-b^2)}$

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

$=\sqrt{1-\frac{1^2}{2^2}}$

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