Answer
Vertices: $(0,±\sqrt 5)$
Eccentricity: $e=\frac{\sqrt 5}{5}$
Work Step by Step
$5x^2+4y^2=20$
$\frac{x^2}{4}+\frac{y^2}{5}=1$
$\frac{x^2}{2^2}+\frac{y^2}{(\sqrt 5)^2}=1$
The major axis is vertical.
Standard form when major axis is vertical:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
So: $a=\sqrt 5$ and $b=2$
$a^2=b^2+c^2$
$c^2=a^2-b^2=5-4=1$
$c=1$
$e=\frac{c}{a}=\frac{1}{\sqrt 5}=\frac{\sqrt 5}{5}$
Vertices when major axis is horizontal:
$(0,±a)=(0,±\sqrt 5)$
