Parallel Tangents to an Ellipse

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This Demonstration shows a construction of parallel tangents to an ellipse in a given direction .


Let and be the foci of the ellipse. Let be the circle with center and radius . Let be the point of intersection with of a line through perpendicular to the direction . Let be the midpoint of and let be symmetric to through the center of the ellipse (the midpoint of ).

Then the perpendiculars to through and are the required tangents.


Contributed by: Izidor Hafner (March 2018)
Open content licensed under CC BY-NC-SA



The proof is left as an exercise.

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