Question

An ellipse has its major axis along y-axis and minor axis along $x$-axis. If its length of latus rectum is $\frac{2}{3}$ times of its minor axis, then the eccentricity of the ellipse is

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{\sqrt{5}}{3}$
• D. $\frac{\sqrt{2}}{5}$

Answer 1

Answer: (C)

Latus rectum of ellipse $=\frac{2}{3}$ (Minor axis)

$ \frac{2 a^2}{b}=\frac{2}{3}(2 a) \Rightarrow \frac{a}{b}=\frac{2}{3} $
$ a=\frac{2}{3} b \Rightarrow a^2=b^2\left(1-e^2\right) $
$ \frac{4 b^2}{9}=b^2\left(1-e^2\right) \Rightarrow e=\frac{\sqrt{5}}{3}$