Folding a Hyperbola

Click the Play button at the lower-left corner of the applet and observe what happens.

The border of the locus of lines formed by the perpendicular bisector of the segment connecting  the point moving on the circle and the fixed point outside the circle forms a hyperbola. The applet below is the simulation of the activity below.

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Activity

1. Draw a circle on a piece of paper.
2. Draw a point outside the circle.
3. Draw an arbitrary point on the circle.
4. Fold the paper such that the at point on the circle and the point outside the circle are coinciding.
5. Repeat steps 3-4 over and over again.

The creases in the paper will form a hyperbola. The construction above is the simulation of this activity.