Final answer:
The equation of the circle with endpoints of the diameter at (2,8) and (4,6) is (x-3)² + (y-7)² = 2.
Step-by-step explanation:
To find the equation of a circle given the endpoints of its diameter, we need to find the center and the radius of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the center is (3,7).
The radius of the circle is half the length of the diameter, which can be found using the distance formula. In this case, the length of the diameter is √[(4-2)² + (6-8)²] = √8 = 2√2. So the radius is √2.
Therefore, the equation of the circle is (x-3)² + (y-7)² = 2.