Let c be the circle in the cordinate plane that passes through the points (0,0) (0,6) and (8,0) what are the cordinates of the center of the circle?

Let
A = (0,0)
B = (0,6)
C = (8,0)

Let point M be the midpoint of segment AB. In this case M = (0,3) since we just average the x and y coordinates of A and B. Similarly, N = (4,0) is the midpoint of segment AC.

Because AB is completely vertical, and because AC is completely horizontal, this means that the center is (4,3). Notice that the x coordinate is drawn from point N and the y coordinate is drawn from point M.

Final (4,3)

See the image attachment for a visual.