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

Answer 1

The general form of a circle is (x - h)² + (y - k)² = r² where the center is at the point (h, k) and the radius is "r". In this case, since the center is at the point (-2, 1), we can write:

(x - (-2))² + (y - (1))² = r² or

(x + 2)² + (y - 1)² = r²

Now, we just need to find the radius. Since the point given is at the same y value as the center, that point is straight over from that center so the radius is 2 (it is 2 units from -2 to -4). That makes the equation:

(x + 2)² + (y - 1)² = 2² or

(x + 2)² + (y - 1)² = 4