Answer
ellipse, center $(-1,1)$, vertices $(-4,1),(2,1)$, and foci $(-1-\sqrt 3,1),(-1+\sqrt 3,1)$.
Work Step by Step
1. Given $2x^2+3y^2+4x-6y=13$ or $2(x+1)^2+3(y-1)^2=18$, thus $\frac{(x+1)^2}{9}+\frac{(y-1)^2}{6}=1$, we can identify the equation as an ellipse with a horizontal major axis, center $(-1,1)$.
2. We have $a=3, b^2=6$ and $c=\sqrt {a^2-b^2}=\sqrt 3$, thus vertices $(-4,1),(2,1)$, and foci $(-1-\sqrt 3,1),(-1+\sqrt 3,1)$.
