For this question you really have to see how much information you can get out of just knowing the endpoints of the diameter.
The y value is the same for both endpoints of the diameter so we know that the given diameter is a horizontal line that is 8 units long because 4 - (-4) = 8, and the radius is 4.
We also know that the center of the circle is the midpoint of the endpoints of the diameter. Halfway between -5 and -5 is -5 so the y value of the midpoint is -5. halfway between -4 and 4 is 0 so the x value of the midpoint must be 0. Thus the center of the circle is (0,-5)
Equation of a circle:
[tex](x-h)^{2} + (y-k)^{2}=r^2 [/tex]
(h,k) is the center of the circle and r is the radius. If you plug in the values of each of these variables, you get the equation of the circle:
[tex](x)^{2} + (y+5)^{2}=16 [/tex]
