equation of a circle that has a center at (h,k) and radius of r is
(x-h)²+(y-k)²=r²
so
given center (-1,2)
(x-(-1))²+(y-2)²=r²
(x+1)²+(y-2)²=r²
sub the other point to find r or r²
it passes through (2,-2)
sub 2 for x and -2 for y
(2+1)²+(-2-2)²=r²
(3)²+(-4)²=r²
9+16=r²
25=r²
5=r
the equation is
(x+1)²+(y-2)²=5²
