the standard equation of a circle is
from your equation a is h and b is K, it would probably be better to use the standard equation since that is what is commonly used.
first find the center of the circle by doing a simultaneous equations of the 2 perpendicular bisectors
of the lines AB and BC
then you have the center C(h,k)
to find the perpendicular bisector of line AB
squaring both sides yields
continue with BC then find H,K by simultanuous equation