The Poncelet directrix-envelope parabola conjecture
Let a Poncelet triangle family be inscribed in a circle, and consider the directrices of its isogonal circumparabolas (CPs). Directrix-envelope parabola conjecture. Over any Poncelet triangle family inscribed in a circle, the envelope of the directrices of the isogonal CPs is a parabola. This is supported by the bicentric, inellipse, MacBeath, and Brocard families described in the source, but the general case remains open.
References
Primary source
Dan Reznik and Ronaldo Garcia, “Poncelet Parabola Pirouettes”, arXiv:2110.06356 (2022).
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