Find the equation of a circle passing through the points (2,-6) (6,4) (-3,1)

you can do this in two ways first method is general one let the equation be x²+y²+ax+by+c=0 and then substituting those points then you get 3 equations and 3 unknowns then you will get required equation
METHOD-2
By using family of circles
first take any 2 points in given three and find eqn of line joining them and next take those 2 points as ends of diameter and construct a circle then family of circles passing through those 2 points is eqn of circle you got =some k times the eqn of line you got and next substitute the third point in that eqn then you get value of k
and finally you end up getting x²+y²+22x-10y-144=0