Question

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity ?

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

Answer 1

The correct option is C $\sqrt{3}/2$

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

Half minor axis $=b$

It is given that the latus rectum and half of minor axis are equal

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

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

Now, $e=\sqrt{1-\left(\frac{b}{a}\right)2}$

$=\sqrt{1-\frac{1}{4}}$

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

Hence, C is correct.