By definition, the general equation for a circle is the one shown below:
[tex]\left(x-h\right)^2+(y-k)^2=r^2[/tex]Where (h,k) is the center of the circle and "r" is the radius.
In this case, you know that the center of the circle is (-7, 1) and its radius is 15. Then, you can identify that:
[tex]\begin{gathered} h=-7 \\ k=1 \\ r=15 \end{gathered}[/tex]Finally, substituting these values into the general equation for the circle shown above and simplifying, you get that the equation of this circle is the following:
[tex]\begin{gathered} \left(x-(-7)\right)^2+(y-1)^2=15^2 \\ (x+7)^2+(y-1)^2=225 \end{gathered}[/tex]