Question

In the ellipse distance between the foci is equal to the distance between a focus and one end of minor axis then its eccentricity is

• A. ${}^{\frac{1}{2}}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A ${}^{\frac{1}{2}}$

Distance between focus and one end is $\sqrt{b^2+a^2{e}^2}$
Given distance between foci is $2ae$
$\Rightarrow 2ae=\sqrt{b^2+a^2{e}^2}$
$3a^2{e}^2=b^2$
$3e^2=\frac{b^2}{a^2}=1-e^2$....................(using relation between a,b,and e)
$4e^2=1$
$e=\frac{1}{2}$