Final answer:
The equation of a circle with center at (-2, 6) and passing through the point (-2, 10) is (x + 2)^2 + (y - 6)^2 = 16.
Step-by-step explanation:
The equation of a circle with center at (-2, 6) and passing through the point (-2, 10) can be found using the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
Substituting (-2, 6) as the center and (-2, 10) as a point on the circle, we get (x + 2)^2 + (y - 6)^2 = r^2.
Since the circle passes through a point on its circumference, the distance between the center and the point is equal to the radius. In this case, the distance is 4. Using the formula for distance, we get (-2 - (-2))^2 + (10 - 6)^2 = 4^2, which simplifies to 4 = 4.
Therefore, the equation of the circle is (x + 2)^2 + (y - 6)^2 = 16.