Answer
$\frac{x^2}{32}+\frac{y^2}{36}=1$
Work Step by Step
Major axis is vertical.
Foci: $(0,±c)=(0,±2)$
$c=2$
$e=\frac{c}{a}$
$\frac{1}{3}=\frac{2}{a}$
$a=6$
$a^2=b^2+c^2$
$b^2=a^2-c^2=6^2-2^2=36-4=32$
$b=4\sqrt {2}$
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{(4\sqrt 2)^2}+\frac{y^2}{6^2}=1$
$\frac{x^2}{32}+\frac{y^2}{36}=1$
