The parallels from {a',b',c'} to the axis of the parabola meet the opposite sides of the anticomplementary triangle on points of the parabola.

In fact, the parallel line L

t=(b

Thus, the y-coordinate of the intersection point is b'

Further, for all directions not coinciding with the sides of ABC the conic is a parabola whereas for directions coinciding with a side of the triangle the corresponding conic degenerates to a set of two parallel lines.

The remarks have a nice consequence for parabolas circumscribing a triangle. See the file CircumconicsTangentToLine.html . Another approach of the same subject is to be found in AllParabolasCircumscribed.html .

CircumconicsTangentToLine.html

Parabola.html

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