Answer
ellipse, center $(1,-1)$, vertices $(1,-4),(1,2)$, foci $(1,-1-\sqrt 5),(1,-1+\sqrt 5)$
Work Step by Step
1. Given $9x^2+4y^2-18x+8y=23$ or $\frac{(x-1)^2}{4}+\frac{(y+1)^2}{9}=1$, we can identify it as an ellipse with a vertical major axis, $a=3, b=2$ and $c=\sqrt {a^2-b^2}=\sqrt 5$.
2. We can find its center $(1,-1)$, vertices $(1,-4),(1,2)$, foci $(1,-1-\sqrt 5),(1,-1+\sqrt 5)$
