We have to find the equation of a circunference with:

As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.
We will find then the radius, by calculating the distance:
![\begin{gathered} d(C,P)=\sqrt[]{(-3-(-6))^2+(7-(-2)_{})^2} \\ =\sqrt[]{(-3+6)^2+(7+2)^2} \\ =\sqrt[]{3^2+9^2} \\ =\sqrt[]{9+81} \\ =\sqrt[]{90} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/wuew4pq4hwj4n8a6jtldokd116hbykcjfc.png)
Now, this means that the radius is √90.
We use the standard form for the equation of a circle:

where (h,k) is the center of the circle. In this case,

And replacing, we obtain that the equation of the circle is:
![\begin{gathered} (x+3)^2+(y-7)^2=(\sqrt[]{90})^2 \\ (x+3)^2+(y-7)^2=90 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/qemxl1ob5pvvw2ez9wrruaotpuo6s9s9vr.png)