Parallel Tangents to an Ellipse
This Demonstration shows a construction of parallel tangents to an ellipse in a given direction .[more]
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.[less]
The proof is left as an exercise.