Find an equation of the circle that has center (-2, 6) and passes through (-6, 2).
The general equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Given that the center is (-2, 6) and the point (-6, 2) lies on the circle, we can substitute these values into the equation:
(-6 - (-2))^2 + (2 - 6)^2 = r^2
(-4)^2 + (-4)^2 = r^2
16 + 16 = r^2
32 = r^2
Therefore, the equation of the circle is:
(x + 2)^2 + (y - 6)^2 = 32