Assume that we want to find the locus of a point. If we prove that three different positions of this point are collinear, then can we say that the locus is the line connecting these positions?
2026-03-27 05:34:33.1774589673
About locus in general
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If your locus is an non-reducable algebraic curve of degree $d$, then it will intersect a line at up to $d$ points. So if $d\geq3$ (e.g. $d=3$, a cubic curve), then you can expect to find three collinear points, although the curve is not a line.