Answer
Vertices: $(0,±3)$
Eccentricity: $e=\frac{2}{3}$
Work Step by Step
$9x^2+5y^2=45$
$\frac{x^2}{5}+\frac{y^2}{9}=1$
$\frac{x^2}{(\sqrt 5)^2}+\frac{y^2}{3^2}=1$
The major axis is vertical.
Standard form when major axis is vertical:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
So: $a=3$ and $b=\sqrt 5$
$a^2=b^2+c^2$
$c^2=a^2-b^2=9-5=4$
$c=2$
$e=\frac{c}{a}=\frac{2}{3}$
Vertices when major axis is horizontal:
$(0,±a)=(0,±3)$
