Since you seemed to be open to Draconis' suggestions, I gather you are not wed to the set-theory idea of a line "containing" a point and are just looking for a way to say the point is on the line (i.e., it is either one of the line's end points or the line goes through it).
In that case, I would suggest: punctum in parabola situm est (situs, -a, -um = placed). Why? Because in such cases my go-to method is to Google what Euler has to say, and Euler has, for example, this to say:
Illustrissimus Auctor ostendit tria horum punctorum E, F et H semper in eadem linea recta fore sita
si tria puncta E, F, G forment triangulum EFG, tum quartum punctum H ita in recta EF producta [drawn out, extrapolated] erit situm, ut sit FH = 1/2 EF
Casus quo quatuor puncta in directum sunt sita
All examples taken from Solutio facilis problematum quorundam geometricorum difficillimorum.
(Sub quo titulo inconspicuo latet una e multis rebus ab Eulero nomen tenentibus, Recta Euleri.)