Find the equation, the center and the radius of a circle passing through (1,-3) , (2,-2) and (-2,6).... with steps.
Each pair of points, and there are three pairs, makes the endpoints of a chord of the circle. The perpendicular bisector of any chord passes through the center of the circle. Once the center is determined, the distance from the center to any one of the points is the radius.
Procedure:
Select two of the points. Using the two-point form of a line, write the equation of the line passing through those two points. Put this equation into slope-intercept form.
Using the mid-point formula, calculate the midpoint of the segment joining the two points.
Find the negative reciprocal of the slope of the line passing through the two points -- this is the slope of any perpendicular. Using this slope and the mid-point, write the equation of the perpendicular bisector of the chord.
Repeat this process for another pair of the given points.
You should now have two equations representing the perpendicular bisectors of two chords of the circle. Solve this system of equations for the point of intersection of the two lines. The solution set will be the center (h,k) of the desired circle.
Using the distance formula, calculate the distance between the center you just derived and any one of the given points. The distance will be the circle radius.