Define a circle, an eccentric point inside the circle and line segments starting from the point and ending at the circle's circumference.
Rotating every line around its mid-point by 90 degrees creates an ellipse with the center of the circle and the point as its focal points.
To run the simulation Processing needs to be installed. After installation open EllipseFromCircle.pde and run. While running, pressing the mouse button sets new point from which the lines are going to be created.
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The topic was mentioned in the video
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The simulation was made in Processing