Final answer:
The equation of the circle with center (3,0) containing the point (-2, √56) is (x - 3)^2 + y^2 = 9.
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is given by the equation:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (3, 0) and the circle contains the point (-2, √56).
To find the radius of the circle, we need to calculate the distance between the center and the given point:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values into the formula:
Distance = √((-2 - 3)^2 + (√56 - 0)^2)
Distance = √(25 + 56)
Distance = √81 = 9
Therefore, the equation of the circle is: (x - 3)^2 + y^2 = 9