Question

The circle drawn on the minor axis as diameter passes through the foci of the ellipse $S=0$, then its eccentricity $e=$

• A. $\sin {18}^0$
• B. $\sin {30}^0$
• C. $\cos {45}^0$
• D. $\cos {30}^0$

Answer 1

Answer: (C)

$\cos {45}^0$

Since, circle with minor axis as diameter passes through foci
$\Rightarrow ae=b$
$e=\frac{b}{a}$
$e^2=\frac{b^2}{a^2}=1-e^2$
$2e^2=1$
$e=\frac{1}{\sqrt{2}}=\cos {45}^{\circ }$