hello :
the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)is :
x² + y² + 4x − 2y + 1 = 0
because :
(x²+4x)+(y²-2y+1)=0
(x²+4x+4) -4 +(y²-2y+1) =0
(x+2)² + (y-1)² = 2².....(the general form )
the center is : (-2 ,1)
passing through (-4, 1) because : x=- 4 and y =1
(-4+2)² + (1-1)² =2²=4... (right)