What is the general form of the equation of a circle at (-2,1) and passing through (-4,1)?

The general form of the equation of a circle with radius ' r '
and centered at  (a, b)  is

                              (x - a)² + (y - b)²  =  r²

I'm pretty sure that your circle is not "at (-2,1)".
I'm going to approach your question assuming that
the circle's center is there.

Since the circle's center is at (-2, 1), the left side of its equation is

                             (x + 2)² + (y - 1)²  =  .

The distance from the center to (-4, 1) is the circle's radius.

That distance is 2, so the right side of the equation is

                                                             4 .