Hyperbola, Ellipse, Circle Construction using Geometry!

What type of triangle is formed by the points "Conic" "Focus2" and "Move"? What do we know about that type of triangle? How do we know that it is that type of triangle (Hint: the red line is the perpendicular bisector of the orange line)?

What do we know about the length of the purple segment compared to the green segment?

Make sure both focus points are inside the circle. What do we know about the sum of the blue and purple segments compared to the sum of the blue and green segments?

Place Focus2 on top of Focus1, and move the point called "Move" around the circle. What shape is made? Try to explain why this shape is made.

Place Focus2 somewhere inside the circle, not on top of Focus 1. Move the point called "Move" around the circle. What shape is made? Try to explain why this shape is made. (Hints: What do we know about the sum of the blue and green segments? What do we know about the sum of the the blue and purple segments? What do we know about the radius of a circle?)

Place Focus2 somewhere outside the circle. Move the point called "Move" around the circle. What shape is made? Try to explain why this shape is made. (Hints: What do we know about the length of the green segment minus the length of the blue segment? What do we know the length of the purple segment? What do we know about the radius of a circle?)