Question

If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance between foci = length of minor axis, then the equation of the ellipse is ...... .

Answer 1

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

$2ae=2b$

$b=ae$

We know, $b^2=a^2(1-e^2)$

$2a^2{e}^2=a^2$

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

Thus, $a=b\sqrt{2}$

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

$b=5\sqrt{2}$

$a=10$

Therefore, the required equation of the ellipse is

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