Question

The length of the latus rectum of an ellipse is one third of the major axis, its eccentricity would be

• A. $2/3$
• B. $\sqrt{\left(2/3\right)}$
• C. $1/\sqrt{3}$
• D. $1/\sqrt{2}$

Answer 1

The correct option is A $2/3$

As per the question

$\frac{2b^2}{a}=\frac{1}{3}\left(2a\right)$

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

Eccentricity is given as

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

$=1-\frac{1}{3}$

$=\frac{2}{3}$