Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the equation as $9x^2-36x-y^2-6y=-36$ or $9(x^2-4x+4)-(y^2+6y+9)=-36+36-9$ which gives $9(x-2)^2-(y+3)^2=-9$
Step 2. Divide both sides by $-9$, we get $\frac{(y+3)^2}{9}-(x-2)^2=1$ which represents a hyperbola centered at $(2,-3)$ with $a=3, b=1$
Step 3. The above hyperbola can be graphed as shown in the figure.
