I'm currently in pre-calc, but my assignment is to figure out and prove which type of conic section I formed by folding a paper circle. My specific instructions were to mark the center of the circle as point C, and mark another point not near the center as point F. Then, repeatedly fold the paper from different points so the edge, or circumference of the circle touches point F until I see a recognizable curve. What I see appears quite plainly to be an ellipse, with points C and F as the foci, but I'm not sure how to prove it.

Additionally I was told to choose a point A on the circumference of the circle and make a line on the crease formed by folding from A to F, then draw a line from A to C, which would be a radius. I notice that the line along the crease is tangent to what appears to be the ellipse. Finally, I'm told to draw a point from A to F to help prove the curve is what I think it is.

I took geometry 2 years ago, and I don't know where to begin proving this.