Question 329434
Use determinants.
|x^2 + y^2  +x  +y  +1|
x1^2+y1^2  x1  y1 +1|
x2^2+y2^2  x2  y2 1| = 0
x3^2+y3^2  x3  y3 1|

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(x1,y1), etc are the 3 points.
It looks messy, but I made an Excel sheet that does them.
It also does parabolas.