Given three points that are not colinear, how do you define a plane such that the circle intersecting these three points lies on the plane? Please define the plane as a function .
Let your 3 points be p1, p2, p3.
Create the vectors (p1-p2), (p1-p3).
Their cross product will be normal to the plane you want to specify. I'll leave it to you to go from the normal vector to your function specification.
Pauls Online Notes : Calculus III - Equations of Planes