> > So the equation becomes either > > C.Y^2 + D.X + E.Y + F = 0 with axis // oX, or > > A.X^2 + D.X + E.Y + F = 0 with axis // oY > > > > In either case 4 points are necessary to determine > > the equation... > > Without loss of genearlty we can divide out the above > by F so that there remain three constants only. > > An inclined axis needs one more constant or one more > point. > Narasimham, Thanks for your comment. You are right that each of these equations has only 3 independent unknowns, but these equations are in the rotated coordinate system and are only to illustrate that, after rotation, we get a parabola with axis // to either oX or oY.
My first post addressed the situation with the parabola axis // oy, requiring only 3 points for determination.
To solve the general problem of how many points are necessary for a parabola of arbitrary orientation, we have the general 2nd degree equation, with 5 independent unknowns, and the equation setting the discriminant =0, leaving 4 independent unknowns to be determined, so we need 4 acceptable points, as you have said.