Answer: the equation represents a circle centered at (-6, -6) with radius 2.
Step-by-step explanation:
x^2 + 12x + 36 + y^2 + 12y + 12 - 36 = 0
Simplifying, we get:
(x + 6)^2 + y^2 - 12 = 0
For the y terms, we add (12/2)^2 = 36 to both sides to get:
x^2 + 12x + 36 + y^2 + 12y + 36 - 24 = 0
Simplifying, we get:
(x + 6)^2 + (y + 6)^2 = 4
Therefore, the equation represents a circle centered at (-6, -6) with radius 2.