The surface of a sphere is defined in that manner.
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It is a parabola.
There will always be a single plane through all three points.
It depends on the context in which the question is asked: whether it is basic geometry, coordinate geometry or vector algebra. If you can draw a single straight line through a set of points they are collinear; if you cannot then they are not.
The slope of a line can be found by choosing any two points of that single line, not of multiple lines.
Collinear points are points that lie on the same line. Noncollinear points do not lie on the same line. Any two points are always collinear, i.e. forming a line. Three or more points can be collinear along a single line.Collinear points lies on the same straight line.