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yes, any three non collinear points will make a circle, however, four or more will not
I think the question you mean to ask is, "Do three collinear points make a triangle?" Linear is simply the adjective form of "line", "collinear" is used to describe points that lie on the same line. (Two points not only can be collinear, but always are, so it makes little sense to describe them as such).Collinear points cannot make a triangle, a triangle requires three noncollinear points.
In general, a linear equation CANNOT be made to go through three points. That will only happen if the three points are collinear and in that case, the equation of the line will only require two points.
The three point line is a line around the perimeter that if you shoot out of it and make it, it counts as 3 points.
No, A plane can be drawn through any 3 points. If the 3 points are collinear then they make a line and a plane can contain a line. If the points are noncollinear then they can be used to form the corners of a triangle; all points of a triangle are in the same plane.