Answer
$\frac{x^2}{5}+\frac{y^2}{9}=1$
Work Step by Step
Major axis is vertical.
Foci: $(0,±c)=(0,±2)$
$c=2$
Vertices: $(0,±a)=(0,±3)$
$a=3$
$a^2=b^2+c^2$
$b^2=a^2-c^2=3^2-2^2=9-4=5$
$b=\sqrt 5$
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{(\sqrt 5)^2}+\frac{y^2}{3^2}=1$
$\frac{x^2}{5}+\frac{y^2}{9}=1$
