The Trammel of Archimedes

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The three blue dots determine the position of the centre, the major axis and the minor axis. Each blue line has length equal to half the sum of the length of the major axis and the minor axis. Click and drag the green point to move this line along the major axis; the other end is automatically drawn to stay on the minor axis. The black point on each blue line is a distance equal to half the minor axis from the green point. The Trammel of Archimedes theorem says that this point always lies on the ellipse.
Similarly, each red line has length equal to half of the length of the major axis. Click and drag the yellow point to move it along the minor axis. The line is automatically redrawn so that it intersects the major axis at a distance equal to half of the difference of the length of the two axes from the yellow point. The Trammel of Archimedes theorem says that the end of the red line (with distance from the yellow point equal to half of the length of the major axis) always lies on the ellipse.