you can do this in two ways first method is general one let the equation be x^{2}+y^{2}+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 x^{2}+y^{2}+22x-10y-144=0