Answer
center $(-3,1)$, foci $(-3-2\sqrt 2,1),(-3+2\sqrt 2,1)$, vertices $(-6,1),(0,1)$
See graph.
Work Step by Step
1. $x^2+9y^2+6x-18y+9=0\Longrightarrow (x+3)^2+9(y-1)^2=9$ or $\frac{(x+3)^2}{9}+\frac{(y-1)^2}{1}=1$,
2. we can find center $(-3,1)$ with a horizontal major axis, $a=3, b=1$, $c=\sqrt {a^2-b^2}=\sqrt {9-1}=2\sqrt 2$,
3. thus foci $(-3\pm2\sqrt 2,1)$ or $(-3-2\sqrt 2,1),(-3+2\sqrt 2,1)$, vertices $(-3\pm3,1)$ or $(-6,1),(0,1)$
4. See graph.
