Answer
$\frac{x^2}{48}+\frac{y^2}{64}=1$
Work Step by Step
Major axis is vertical.
$(0,±8)=(0,±a)$
$a=8$
$e=\frac{c}{a}$
$\frac{1}{2}=\frac{c}{8}$
$2c=8$
$c=4$
$a^2=b^2+c^2$
$b^2=a^2-c^2=8^2-4^2=64-16=48$
$b=4\sqrt 3$
Standard form when major axis is vertical:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{(4\sqrt 3)^2}+\frac{y^2}{8^2}=1$
$\frac{x^2}{48}+\frac{y^2}{64}=1$
