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

The general form of the equation of a circle with its center at (a, b) is

           (x - a)²  +  (y - b)²  =  (radius)² .

So if the center of your circle is at (-2, 1)
we know that the left side of the equation is

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

For the right side of the equation, we need to know the circle's radius.

Well, you said that the point  (-4, 1) is on the circle.
How far is that point from the center at  (-2, 1) ?

It looks to me like the distance between (-2, 1) and (-4, 1) is 2 units.
So the radius of the circle is  2 , and the full equation is ...

               (x + 2)²  +  (y - 1)²  =  4  .

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