Answer:
The equation of the circle with center (0, -6) containing the point (-√28, 3) is x^2 + (y + 6)^2 = 109.
Explanation:
The equation of a circle with center (h, k) and radius r is given by the formula:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -6), which means that h = 0 and k = -6. We also know that the circle contains the point (-√28, 3), which means that this point is on the circle and satisfies the equation above.
To find the radius r, we can use the distance formula between the center of the circle and the given point:
r = sqrt((0 - (-√28))^2 + (-6 - 3)^2) = sqrt(28 + 81) = sqrt(109)
Substituting h, k, and r into the equation of the circle, we get:
x^2 + (y + 6)^2 = 109
Therefore, the equation of the circle is x^2 + (y + 6)^2 = 109.