Put the constant on the right side, then group the $x$ terms together and the $y$ terms together.

For $x^2+8x$, add and subtract $(\tfrac{8}{2})^2$. For $y^2-6y$, add and subtract $(\tfrac{-6}{2})^2$.

In Desmos, enter $x^2+y^2+8x-6y-11=0$ to graph the circle.

Enter one answer choice, such as $(x+4)^2+(y-3)^2=36$, and see whether it matches the original circle exactly.

The correct choice is the one whose graph lies exactly on top of the graph from the original equation.

Start with

Move the constant term to the other side and group:

Complete the square for each variable:

• $x^2+8x=(x+4)^2-16$
• $y^2-6y=(y-3)^2-9$

Substitute:

Add $16$ and $9$ to both sides:

So the circle’s equation is $(x+4)^2+(y-3)^2=36$.