Question

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

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

Answer 1

Answer: (A)

$\frac{2}{3}$

Answer 2

As per the question
$\frac{2 b^{2}}{a}=\frac{1}{3}(2 a)$
$\frac{b^{2}}{a^{2}}=\frac{1}{3}$
Eccentricity is given as
$e ^{2} =1-\frac{ b ^{2}}{ a ^{2}}$
$=1-\frac{1}{3}$
$=\frac{2}{3}$