Question

Find equation of ellipse whose vertex are $(0,\pm 10)$ & $e=4/5$

Answer 1

Vertex $(0,\pm 10)$ and $e=\frac{4}{5}$

Equation of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$a=10$

$b=a\sqrt{1-e^2}=10\sqrt{1-(\frac{4}{5}{)}^2}=10\ast \frac{3}{5}=6$

Equation of ellipse $\frac{x^2}{100}+\frac{y^2}{36}=1$