Question

If the minor axis of an ellipse is equal to the distance between its foci then eccentricity is $\frac{1}{\sqrt{2}}$.

• A. True
• B. False

Answer 1

The correct option is A True

Distance between the foci i $2ae$

Length of the minor axis $=2b$

$\therefore$ $2ae=2b$

$\Rightarrow$ $ae=b$

$\Rightarrow$ $b^2=a^2(1-e^2)$

$\Rightarrow$ $a^2{e}^2=a^2-a^2{e}^2$

$\Rightarrow$ $2a^2{e}^2=a^2$

$\Rightarrow$ $e^2=\frac{1}{2}$

$\Rightarrow$ $e=\frac{1}{\sqrt{2}}$

Hence, eccentricity of the ellipse $=\frac{1}{\sqrt{2}}$