Question

Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is $10$.

Answer 1

Given : $2b=2ae$

We have $b=ae$

and $(ae{)}^2=a^2-b^2$

$\Rightarrow b^2=a^2-b^2$

$\Rightarrow \frac{b}{a}=\frac{1}{\sqrt{2}}$

Also given,

$\frac{2b^2}{a}=10$

we get, $b=5\sqrt{2}$

and $a=10$

The equation becomes,

$\frac{x^2}{100}+\frac{y^2}{50}=1$

$\Rightarrow x^2+2y^2=100$