MATHEMATICS AND ORIGAMI

Mathematics and Origami

It means that any other point on AB but T, does not fulfil the condition of being on the ellipse.
Hence AB is the tangent and T its point of tangency.

Fig. 3 displays a very special straight line: it is the ellipse directrix d corresponding to focus F.
The directrix is a rather unknown line in the ellipse, though not in the parabola. Let ́s look at Fig. 4 and
see certain things about it.

To start with, d is the polar of F.
This means that d is the locus of the poles of all the straight lines passing through F; e.g. P 1 is
the pole of LM (polar of P 1 ) with P 1 L and P 1 M tangents to the ellipse.

1

F ́ F

T P

O

A

B

S

cd

2

3

cp

d

F ́ O

F

4

P

P ́ ́

P

P ́

L

M

1

2

O

L

P ́

F ́

5

M

F

P 2 P ́ ́ P 1

d

d

X