Question

Find the equation of an ellipse whose vertices are $(0,\pm 10)$ and $e=\frac{4}{5}$.

Answer 1

Let equation be $\frac{x}{b^2}+\frac{y}{a^2}=1$

And, its vertices are $(0,\pm a)$ and $a=10$

Let $c^2=a^2-b^2$

Then, $e=\frac{c}{a}$

$c=ae=10\times \frac{4}{5}=8$

$b^2=a^2-c^2=100-64=36$

$a^2=100$ and $b^2=36$

Hence, the equation is $\frac{x^2}{36}+\frac{y^2}{100}=1$