Let P (x. y) be any point on the circle. Then APB is a right angled triangle. AP is perpendicular to PB.
If m1 and m2 are the slopes of AP and PB then m1*m2 = -1.
Expand and get the equation of the circle.
You have already been given the procedures but appear to need more help.
Plot the two points and draw AB. AB is the diameter of a circle and its midpoint is the center.Draw the slope diagram for AB.Note that the rise is 4 and the run is 2.Circle diameter is 2rad5 and radius is rad5.Using similar triangles the midpoint of AB is 5,1. Now write the circle equation as shown by others.