Answer
Vertices: $(0,±8)$
Eccentricity: $e=\frac{3}{4}$
Work Step by Step
$16x^2+7y^2=448$
$\frac{x^2}{28}+\frac{y^2}{64}=1$
$\frac{x^2}{(2\sqrt 7)^2}+\frac{y^2}{8^2}=1$
The major axis is vertical.
Standard form when major axis is vertical:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
So: $a=8$ and $b=2\sqrt 7$
$a^2=b^2+c^2$
$c^2=a^2-b^2=64-28=36$
$c=6$
$e=\frac{c}{a}=\frac{6}{8}=\frac{3}{4}$
Vertices when major axis is horizontal:
$(0,±a)=(0,±8)$
