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