Drawing an Ellipse using Archimedes' Trammel

This ellipse drawer, attributed to Archimedes, is the trammel construction. The point B on segment AP is attached to the horizontal axis in such a way that it can slide along the axis. Similarly, the point A is attached to the vertical axis and allowed to slide along it.

Click the Play button at the lower left hand corner to generate the curve. What should be the lengths of BP and AB so that the curve generated will have x intercepts at (±5,0) and y intercepts at (0,±3)? Use the sliders to set a and b to these values and verify that the resulting curve has the correct intercepts. Enter the equations that you found in Exercise 1 into the input field to verify that Archimedes's ellipse drawer does generate an ellipse.