Answer
$\frac{x^2}{16}+\frac{y^2}{25}=1$
Work Step by Step
Major axis is vertical.
Foci: $(0,±c)=(0,±3)$
$c=3$
Vertices: $(0,±a)=(0,±5)$
$a=5$
$a^2=b^2+c^2$
$b^2=a^2-c^2=5^2-3^2=25-9=16$
$b=4$
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{4^2}+\frac{y^2}{5^2}=1$
$\frac{x^2}{16}+\frac{y^2}{25}=1$
