Question

An ellipse whose axis is along $x$ axis and centre at origin. If the distance between focii is equal to length of minor axis, then the eccentricity of the ellipse is

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

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}$

Length of minor axis = distance between focii,
$2b=2ae\Rightarrow e=\frac{b}{a}...........\left(i\right)$
We know that,
$e^2=1-\frac{b^2}{a^2}$
Using equation $\left(i\right),$
$\Rightarrow e^2=1-e^2\Rightarrow 2e^2=1\Rightarrow e=\frac{1}{\sqrt{2}}$