Question

$P$ and $Q$ are the foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $B$ is an end of the minor axis. If $△PBQ$ is an equilateral triangle, the eccentricity of the ellipse is:

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

Answer 1

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

Since the $△PBQ$ is equilateral then,

All sides are $2ae$

And, $PB+BQ=2a$

$\Rightarrow 4ae=2a$

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