Poncelet's Porism

Construct an animation demonstrating Poncelet's Porism for circles: If two circles are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn.

Modify the above situation to the case when the word "circumscribe" also means the extension of the sides of the triangle circumscribing the circle.

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other, then there are infinitely many such quadrilaterals can be so drawn.

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other exteriorly, then there are infinitely many such quadrilaterals can be so drawn.

Construct an animation demonstrating: If a circle and a parabola are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn.

Construct an animation demonstrating: If a circle and a parabola are so related that a triangle can be inscribed to the parabola and circumscribed to the circle externally, then there are infinitely many such triangles can be so drawn.

Construct an animation demonstrating: If an ellipse and a parabola are so related that a quadrilateral can be inscribed to the ellipse and circumscribed to the parabola externally, then there are infinitely many such quadrilaterals can be so drawn.

Construct an animation demonstrating: If two parabolas are so related that a quadrilateral can be inscribed to one and circumscribed to the other externally, then there are infinitely many such quadrilaterals can be so drawn.

Construct an animation showing if there exists one inscribed "star" of a given ellipse tangent to a fixed ellipse, then there are infinitely many inscribed "stars" of the ellipse having the same property.