Final answer:
To determine the radius of the circle, we find the center by finding the mid-point of the line segment AB. The distance from the center to either A or B is the radius r, which is sqrt(13). The general equation of the circle is (x - 4)^2 + (y - 5)^2 = 13.
Step-by-step explanation:
To determine the radius of a circle passing through points A(6, 2) and B(2, 8), we first need to find the center of the circle. Since the circle passes through the mid-point of the line segment AB, we can find the center by finding the mid-point of AB. The mid-point is given by the average of the x-coordinates and the average of the y-coordinates, which is ((6+2)/2, (2+8)/2) = (4, 5).
The distance from the center to either A or B is the radius r. Using the distance formula, we get: sqrt((6-4)^2 + (2-5)^2) = sqrt(4+9) = sqrt(13).
Therefore, the radius of the circle is sqrt(13).
The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Substituting the values (4, 5) for (h, k) and sqrt(13) for r, we get the general equation of the circle as (x - 4)^2 + (y - 5)^2 = 13.