Poncelet Parabola Pirouettes

Using graphical simulation, we observe the motion of parabolas inscribed and circumscribed about certain Poncelet triangle families. In doing so one is surprised by the fact that most parabolas' key objects such as vertex, directrix, focus, perspector, polar triangle, etc., will often sweep (or envelop) surprisingly simple curves, such as lines, circles, points, etc. We revisit some three-dozen such curious observations. Since most are without proof we very much welcome reader contributions.