So the equation is:
$ x^2 + 2y^2 - 6x + 4y + 7 = 0 $
Find the coordinates of the center, the foci, and the vertex or vertices.
What I did was put the equation in the form: $ \frac{(x-3)^2}{4}+ \frac{(y+1)^2}{4} = 1 $
Now based on that, I said the center is at $(3,-1)$, the foci is at ~+- 2.45 (since $c = \sqrt {a^2 + b^2}$ ). so the coordinates of that are $(3+2.45,-1)$ and $(3-2.45,-1)$ and the vertices are $(1,-1)$ and $(5,-1)$. I also went ahead and found the asymptote, which is just done by setting the equation to $0$, correct?