Take into account that the general equation of a circumference is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle and r the radius.
To determine the center of the circle calculate the coordinates of the midpoint between the endpoints of the diameters:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2}=\frac{-3+9}{2}=\frac{6}{2}=3 \\ y=\frac{y_1+y_2}{2}=\frac{6+6}{2}=\frac{12}{2}=6 \end{gathered}[/tex]hence, the midpoint is (h,k) = (3,6) and it is the center of the circle.
To determine the radius of the circle, find first the lengh of the diameter, as follow:
[tex]\begin{gathered} d=\sqrt[]{(-3-9)^2+(6-6)^2} \\ d=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the radius is:
r = d/2 = 12/2 = 6
By replacing the previous values of h, k and r into the general equation for a circle, you obtain:
[tex]\begin{gathered} (x-3)^2+(y-6)^2=6^2 \\ (x-3)^2+(y-6)^2=36 \end{gathered}[/tex]