Answer : (8,5)
Given
K(x) =
Now we plug in each point and check whether it satisfies our equation
(-64,12)
K(-64) = = 12 so this point lie on graph
(125,3)
K(125) = = 3 so this point lie on graph
(343,1)
K(343) = = 1 so this point lie on graph
(8,5)
K(8) = = 6 so this point does not lie on graph because we got 6 instead of 5
so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.