The equation of a circle with center (h,k) and radius r is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]From the question, it is given that the center of the circle is (-7,-4) and the diameter is 8.
Since the radius is half the diameter, it follows that the radius is:
[tex]\frac{\text{diameter}}{2}=\frac{8}{2}=4[/tex]So it implies that r=4, h=-7, and k=-4.
Substitute these values into the equation of a circle:
[tex]\begin{gathered} (x-(-7))^2+(y-(-4))^2=4^2 \\ \Rightarrow(x+7)^2+(y+4)^2=16 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex](x+7)^2+(y+4)^2=16[/tex]