Parallel Tangents to an Ellipse

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.

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The proof is left as an exercise.
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