Two-Pins-and-a-String Construction

Using GSP

(Taken from Key Curriculum Press)

1. Construct aline and hide its control points. Construct points A, B, C on the line such that C lies between A and B.

2. Hide the line and construct line segments AC and CB.

3. Construct and label points F1 and F2 to represent the foci of your ellipse.

4. Construct a circle with center F1 and radius AC. Construct another circle with center F2 and radius CB.

5. Construct the two intersection points of the circles. You might have to adjust your model so that the circles intersect. Select the intersection points and choose Trace Locus from the Display Menu.

6. Drag point C back and forth along segment AB. The trace of the two points should be an ellipse.


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