Answer
$\frac{x^2}{4}+\frac{y^2}{8}=1$
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 $(2,0)$
$\frac{2^2}{b^2}+\frac{0^2}{a^2}=1$
$2^2=b^2$
$b=2$
Foci: $(0,±c)=(0,±2)$
$c=2$
$a^2=b^2+c^2=2^2+2^2=4+4=8$
$a=2\sqrt 2$
$\frac{x^2}{2^2}+\frac{y^2}{(2\sqrt 2)^2}=1$
$\frac{x^2}{4}+\frac{y^2}{8}=1$
