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

The equation of a circle is (x - h)² + (y - k)² = radius²
where the center is represented by (h, k).

So to plug in:
(x - (-2))² + (y - 1)² = radius²
(x + 2)² + (y - 1)² = radius²

To find the radius, you can do the distance formula OR (and I suggest this one) use common sense. The center and point given have the same Y-value meaning they are in a horizontal line. Because of this, you can just find the distance between them (AKA your radius) by doing the absolute value of their difference:

|- 4 - (-2)| = |- 4 + 2| = |-2| = 2

Just to show order doesn't matter:
|- 2 - (-4)| = |- 2 + 4| = |2| = 2

Your radius is 2. Plug this into your equation and simplify.

(x + 2)² + (y - 1)² = (2)²

Your answer is:
(x + 2)² + (y - 1)² = 4