%% auteur : gh
%% conique_ellipse_pythagore.jps
1000 setwidth
600 setheight
-2.5 2.5 setxrange
-1.5 1.5 setyrange

/O {0 0} def
/a 2 def
/b 1 def
/c {a 2 exp b 2 exp sub sqrt} def
/F {c neg 0} def
/F' {c 0} def
/Dx {a 2 exp c div neg 0} def
/Dx' {a 2 exp c div 0} def
/D {Dx Dx 0 1 addv} def
/D' {Dx' Dx' 0 1 addv} def

/X {Cos a mul} def
/Y {Sin b mul} def

traceaxes
axesarrow
<tex>
$$O$$
</tex>
O [3 dup] dltexlabel

6 setlinewidth
rouge
O F' (-) line
O 0 b (-) line
F' 0 b (-) line
F' O 0 b angledroit

2 setlinewidth
noir
/dy {0 0.1} def
/dx {0.1 0} def
O dy subv F' dy subv (<->) line
<tex>
$$c$$
</tex>
O dy subv F' dy subv milieu [3 dup] dctexlabel
O dx subv 0 b dx subv (<->) line
<tex>
$$b$$
</tex>
O dx subv 0 b dx subv milieu [3 dup] cltexlabel
0 b dx dy addv addv F' dx dy addv addv (<->) line
<tex>
$$a$$
</tex>
0 b dx dy addv addv F' dx dy addv addv milieu [3 dup] urtexlabel


2 setlinewidth
vert
0 pi 2 mul settrange
{X} {Y} courbeparam

2 setlinewidth
continu
bleu
[F F'] points
D droite
D' droite
<tex>
$$F$$
</tex>
F [3 dup] dctexlabel
<tex>
$$F'$$
</tex>
F' [3 dup] drtexlabel
<tex>
$$D$$
</tex>
Dx 0 1.5 subv [3 dup] urtexlabel
<tex>
$$D'$$
</tex>
Dx' 0 1.5 subv [3 dup] urtexlabel