Answer
center $(1,-2)$, foci $(1,-2-\sqrt 5),(1,-2+\sqrt 5)$, vertices $(1,-5),(1,1)$
See graph.
Work Step by Step
1. $9x^2+4y^2-18x+16y-11=0\Longrightarrow 9(x-1)^2+4(y+2)^2=36$ or $\frac{(x-1)^2}{4}+\frac{(y+2)^2}{9}=1$,
2. we can find center $(1,-2)$ with a vertical major axis, $a=3, b=2$, $c=\sqrt {a^2-b^2}=\sqrt {9-4}=\sqrt 5$,
3. thus foci $(1,-2\pm\sqrt 5)$ or $(1,-2-\sqrt 5),(1,-2+\sqrt 5)$, vertices $(1,-2\pm3)$ or $(1,-5),(1,1)$
4. See graph.
