Here is a figure resulting as in the discussion to be found in MaclaurinLike.html by relaxing from the condition for the three points {A,B,C} to be collinear. As P describes the given conic c, E is defined to be the intersection of BP with the fixed line L and Q is the intersection of lines {AP, CE}. As was shown in the aforementioned reference, if {A,B,C} are collinear then Q describes a conic. The following picture illustrates the case where the three points {A,B,C} are not collinear. The curve is not in general a conic.

Problem To find the equation of the curve described by Q in dependence from {A,B,C,c,L}.