Answer
multiple answers; see details
Work Step by Step
The standard form of the equation $
3x^2+3y^2+18x-12y=-12
$ is
\begin{array}{l}
x^2+y^2+6x-4y=-4\text{... divide both sides by $3$}\\\\
(x^2+6x)+(y^2-4y)=-4\\\\
(x^2+6x+9)+(y^2-4y+4)=-4+4+9\\\\
(x+3)^2+(y-2)^2=9
.\end{array}
The graph of this equation is a $\text{
circle
}$ with the following properties:
\begin{array}{l}
\text{Center: }\left(
-3,2
\right),\\\\\text{Radius: }
3
.\end{array}
Using the properties above, the graph of the equation is given below.
