Final answer:
The given equation is a circle's equation where 9 is the square of the radius. The radius is 3, therefore, the diameter of the circle is 6.
Step-by-step explanation:
The given equation is in the form of a circle's equation, which is usually represented as (x-a)^2 + (y-b)^2 = r^2 where 'a' and 'b' are the coordinates of the center, and 'r' is the radius of the circle. In the given equation (x+12)^2 + (y+3)^2 = 9, 9 is the square of the radius, meaning that the radius (r) is 3. The diameter of a circle is twice its radius. Thus, for this equation, the diameter is 2*r = 2*3 = 6.
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