Answer
center $(0,-2)$, foci $(0,-2-\sqrt 3),(0,-2+\sqrt 3)$, vertices $(0,-4),(0,0)$
See graph.
Work Step by Step
1. $4x^2+y^2+4y=0\Longrightarrow 4(x)^2+(y+2)^2=4$ or $\frac{(x)^2}{1}+\frac{(y+2)^2}{4}=1$,
2. we can find center $(0,-2)$ with a vertical major axis, $a=2, b=1$, $c=\sqrt {a^2-b^2}=\sqrt {4-1}=\sqrt 3$,
3. thus foci $(0,-2\pm\sqrt 3)$ or $(0,-2-\sqrt 3),(0,-2+\sqrt 3)$, vertices $(0,-2\pm2)$ or $(0,-4),(0,0)$
4. See graph.
