The center-radius form of the circle equation is in the format :
[tex](x-h)^2+(y-k)^2=r^2[/tex]where h and k are the coordinates of the centere and r is the radius of the circlle.
In the given equation:
[tex](x+4)^2+(y-1)^2=32[/tex]we can see that :
[tex]\begin{gathered} h=-4 \\ k=1 \\ r^2=32 \end{gathered}[/tex]Thus, the coordinates of the center of the circle is:
[tex]C(-4,1)[/tex]