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