The center of a circle is located at (--2,7). The radius of the circle is 2.

We have

(x + 2)^2  +  ( y - 7)^2  =   4          expand

x^2  + 4x  + 4   +  y^2  - 14y  +  49    = 4          subtract 4 from both sides

x^2 + y^2  + 4x  - 14y  +  49   = 0