Final answer:
The coordinates of the center of the circle are (8, -2). The radius of the circle is 10. The equation of the circle is (x - 8)² + (y + 2)² = 100.
Step-by-step explanation:
To find the coordinates of the center of the circle, we can use the midpoint formula. The midpoint is the average of the x-coordinates and the average of the y-coordinates. So, the x-coordinate of the center is (2 + 14)/2 = 8, and the y-coordinate of the center is (6 + -10)/2 = -2. Therefore, the coordinates of the center of the circle are (8, -2).
To calculate the radius of the circle, we can use the distance formula. The distance between the endpoints of the diameter is the diameter of the circle. So, the radius is half the length of the diameter. Using the distance formula, the length of the diameter is √((14 - 2)² + (-10 - 6)²) = 20. Therefore, the radius of the circle is 20/2 = 10.
The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle, and r represents the radius. Substituting the values we found, the equation of the circle is (x - 8)² + (y - (-2))² = 10².