Step 1: Note down the given center and points.

NOTE: Assume that (x, y) are the coordinates of a point on the circle shown. The center is at (h,k), and the radius is r.  

Step 2: Calculate the given circle radius  

          NOTE: Radius = distance between center and point on the surface of the circle. So, use the Distance formula to find the equation of the circle.

                          d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\

          EXAMPLE:Given points (2, 1)(10, 7)

                    r\ =\ \sqrt{\left(10\ -\ 2\right)^2\ +\ \left(7-2\right)^2}

                  r = \sqrt{ 64 - 36}

                           r =\sqrt{100}

Step 3: Substitute this values in the equation of a circle.

NOTE: Standard Form for the equation of the circle

  (x - h)^2 + (y - k)^2 = r^2

Where center (h, k) and r- radius

EXAMPLE: (x-2)_{\ \ }^2+(y-1)^2=\ 100

Step 4: Simplify the equation further