# Parallel Tangents to an Ellipse

Parallel Tangents to an Ellipse

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

ϕ

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 ).

F

1

F

2

σ

F

1

2a

P

σ

F

2

ϕ

N

1

P

F

2

N

2

N

1

F

1

F

2

Then the perpendiculars to through and are the required tangents.

PF

2

N

1

N

2