The general equation of a circle is
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ Where (h,k) are the coordinates of the center and} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} r=2 \\ h=-3 \\ k=2 \end{gathered}[/tex][tex]\begin{gathered} (x-(-3))^2+(y-2)^2=(2)^2 \\ (x+3)^2+(y-2)^2=4 \end{gathered}[/tex]Therefore, the equation for this circle is
[tex](x+3)^2+(y-2)^2=4[/tex]and the correct answer is option C.
