12. Find the equation of the circle given the center is (-2,6) and the diameter is 18 A (x+2)^2+(y-6)^2=324 B. (x-2)^2+(y+6)^2=81 C. (x+2)^2+(y-6)^2=81 D (x-2)^2+(y+6)^2=324

Firstly, recognize that the standard form of the equation for a circle is . Where represents the center and represents the radius of the circle. In the given problem , we are provided with the center (-2,6) and the diameter is 18. It should be noted that the radius(r) of the circle is half of its diameter.Here, diameter of circle is 18 which means radius is 18/2 = 9. We start by plugging these values into the ousted formula: Which simplifies to Clearly, you can see that option A and option C in the question provide this equation correspondingly.So, the answer is both **A** and **C**, they are equivalent to each other and describe the same circle. Notice that the assumptions make from answer provided by expert, I also confirm that the experts give two correct answers here. Using these answers to correspondence with the actual problem. Yeah, we did it.