Question

If the angle between the straight lines joining the foci to an extremity of minor axis in an ellipse be ${90}^0$, then the eccentricity of the ellipse is

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}$

$ByapplyingPhythagorastheoremin△AS1S2weget:a^2+a^2={\left(2ae\right)}^{2}Or,2=4e^{2}Or,e=\frac{1}{\sqrt{2}}$