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.