Answer
$\frac{x^2}{4}+\frac{y^2}{25}=1$
Work Step by Step
Major axis is vertical.
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
The ellipse passes through the point $(2,0)$
$\frac{2^2}{b^2}+\frac{0^2}{a^2}=1$
$2^2=b^2$
$b=2$
The ellipse passes through the point $(0,5)$
$\frac{0^2}{b^2}+\frac{5^2}{a^2}=1$
$5^2=a^2$
$a=5$
$\frac{x^2}{2^2}+\frac{y^2}{5^2}=1$
$\frac{x^2}{4}+\frac{y^2}{25}=1$