Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as
$4(x^2+6x+9)+9(y^2-4y+4)=36+36-36$
or
$\frac{(x+3)^2}{9}+\frac{(y-2)^2}{4}=1$
We can identify
$a=3, b=2, c=\sqrt {9-4}=\sqrt 5$
with a center at $(-3,2)$
Step 2. See graph; we can locate the foci at $(-3\pm\sqrt 5,2)$
