Question

An ellipse having foci at $(3,1)$ and $(1,1)$ passes through the point $(1,3)$. Then find its eccentricity.

Answer 1

Answer: 0.41

$PS+P{S}^{\prime }=2a$
$\sqrt{4+4}+2=2a$
$2(\sqrt{2}+1)=2a$
$\Rightarrow a=\sqrt{2}+1$
$2ae=\sqrt{4+0}$
$\Rightarrow 2ae=2$
$\Rightarrow ae=1$
$e=\frac{1}{\sqrt{2}+1}\times \frac{\sqrt{2}-1}{\sqrt{2}-1}$
$e=\sqrt{2}-1$