Answer
center $(-1,1)$, foci $(-1,0),(-1,2)$, vertices $(-1,-1),(-1,3)$
See graph.
Work Step by Step
1. $4x^2+3y^2+8x-6y=5\Longrightarrow 4(x+1)^2+3(y-1)^2=12$ or $\frac{(x+1)^2}{3}+\frac{(y-1)^2}{4}=1$,
2. we can find center $(-1,1)$ with a vertial major axis, $a=2, b=\sqrt 3$, $c=\sqrt {a^2-b^2}=\sqrt {4-3}=1$,
3. thus foci $(-1,1\pm1)$ or $(-1,0),(-1,2)$, vertices $(-1,1\pm2)$ or $(-1,-1),(-1,3)$
4. See graph.
