Editing Pascal's theorem (section)

== Degenerations of Pascal's theorem ==
[[File:Pascal-3456.png|450px|thumb|Pascal's theorem: degenerations]]
There exist 5-point, 4-point and 3-point degenerate cases of Pascal's theorem. In a degenerate case, two previously connected points of the figure will formally coincide and the connecting line becomes the tangent at the coalesced point. See the degenerate cases given in the added scheme and the external link on ''circle geometries''. If one chooses suitable lines of the Pascal-figures as lines at infinity one gets many interesting figures on [[parabola#Properties of a parabola related to Pascal's theorem|parabolas]] and [[Hyperbola#As an affine image of the hyperbola y = 1/x|hyperbolas]].