First use the standard form:
\((x-h)^2+(y-k)^2=r^2\)
(h,k) - the coordiantes of the center
The center is (-2,1).
\((x-(-2))^2+(y-1)^2=r^2 \\
(x+2)^2+(y-1)^2=r^2\)
The circle passes through the point (x,y)=(-4,1).
\((-4+2)^2+(1-1)^2=r^2 \\
(-2)^2+0^2=r^2 \\
r^2=4\)
The standard form is:
\((x+2)^2+(y-1)^2=4\)
Convert it to the general form:
\((x+2)^2+(y-1)^2=4 \\
x^2+4x+4+y^2-2y+1=4 \\
x^2+y^2+4x-2y+4+1-4=0 \\
\boxed{x^2+y^2+4x-2y+1=0}\)
