答案：D

解析：

Choice D is correct.

The equation for a circle with a center at (h,k) and a radius of r is:

(x-h)^2+(y-k)^2=r^2

The length of the radius is half of the length of the diameter.

1/2*18 =9

Filling in the coordinates of the center and the length of the radius of this circle results in the equation:

(x-1)^2+(y-(-6))^2=9^2

In standard form, the equation of this circle is: (x-1)^2+(y+6)^2=81