Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as
$9(x^2-2x+1)+4(y^2+2y+1)=9+4+23$
or
$\frac{(x-1)^2}{4}+\frac{(y+1)^2}{9}=1$
We can identify
$a=3, b=2, c=\sqrt {9-4}=\sqrt 5$
with a center at $(1,-1)$
Step 2. See graph; we can locate the foci at $(1,-1\pm\sqrt 5)$
