Here is just another demonstration of a relationship between an ellipse and two special concentric circles. Two points will rotate around the circles at equal speeds in opposite directions. The midpoint between them will be traced. Those rotating points will start at the top of the circles if the vertical axis is longer than the horizontal axis. Otherwise the rotating points start "due east" from the center.
Play around.
The original file is here. Download it and experiment. GeoGebra is cool!
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