Parallel Tangents to an Ellipse

semiaxes

a

0.6

b

0.45

direction of tangent

ϕ

0.45

zoom

2

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

ϕ

.

Let

F

1

and

F

2

be the foci of the ellipse. Let

σ

be the circle with center

F

1

and radius

2a

. Let

P

be the point of intersection with

σ

of a line through

F

2

perpendicular to the direction

ϕ

. Let

N

1

be the midpoint of

P

F

2

and let

N

2

be symmetric to

N

1

through the center of the ellipse (the midpoint of

F

1

F

2

).

Then the perpendiculars to

PF

2

through

N

1

and

N

2

are the required tangents.