6 problems

Let $\cal{P}$ be a parabola, let $\cal{C}$ be a focus-centered circle, and let $\cal{R}$ be a Poncelet family of $N$-gons inscribed in $\cal{P}$ and circumscribed about $\cal{C}$.…

Let $\cal{P}$ be a parabola and $\cal{C}$ a focus-centered circle, and let $\cal{R}$ be a Poncelet family of $N$-gons inscribed in $\cal{P}$ and circumscribed about $\cal{C}$. Gene…

Let $\cal{P}$ be a parabola and consider the family of polar polygons associated with parabola-inscribed Poncelet pentagons. Polar-pentagon centroid-locus conjecture. The loci of t…

Let $\cal{P}$ be a parabola of focal distance $f$, and let $\cal{C}$ be a focus-centered circle of radius $r$ such that they admit a Poncelet family of inscribed pentagons. Pentago…

Let $X_k'$ denote a triangle center of the polar family, and suppose its locus is a circle with nonzero radius. Circular-locus pencil conjecture. That circle belongs to the parabol…

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 Poncel…