Answer
$\frac{x^2}{25}+\frac{y^2}{50}=1$
Work Step by Step
Minor axis: $Length=2b$
$2=10$
$b=5$
Foci on y-axis: major axis is vertical.
Use the point $(\sqrt 5,\sqrt {40})$.
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{(\sqrt 5)^2}{5^2}+\frac{(\sqrt {40})^2}{a^2}=1$
$\frac{1}{5}+\frac{40}{a^2}=1$
$\frac{40}{a^2}=1-\frac{1}{5}=\frac{4}{5}$
$4a^2=200$
$a^2=50$
$a=5\sqrt 2$
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{5^2}+\frac{y^2}{(5\sqrt 2)^2}=1$
$\frac{x^2}{25}+\frac{y^2}{50}=1$