Let's review this
Geometry
Level
3
Given any 3 non collinear points in the 2D plane, at most how many parabolas can be made to pass through these 3 points?
Infinitely many
2
3
Cannot be determined
1
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1 solution
Given any 3 points, there is still another variable left unconsidered in constructing the parabola passing through it.. that is the axial direction . The fact that most books say that there is a unique parabola passing through these points is because of the assumption that it is facing (or opening) towards one of the standard axes, most commonly y. If this is otherwise stated, we can construct other parabolas opening through any direction, still passing through these 3 points.