$(x-2)^2+(y-6)^2=49$ $C(2,6), r=7$ See graph.
Work Step by Step
Step 1. From the given equation $x^2+y^2-4x-12y-9=0$, we have $(x^2-4x+4)+(y^2-12y+36)=4+36+9$ and $(x-2)^2+(y-6)^2=49$ Step 2. We can identify the center and radius of the circle as $C(2,6), r=7$ Step 3. See graph.