%% auteur : gh
%% conique_ellipse_tangente.jps
1000 setwidth
666 setheight
-2.5 5 setxrange
-2.5 2.5 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
0 pi 2 mul settrange
{X} {Y} courbeparam

bleu
O a cercle

3 setlinewidth
/t {pi 3 div} def
/M {t dup X Y} def
/N {t Cos a mul t Sin a mul} def
/P {t Cos a mul 0} def

noir
<tex>
$A$
</tex>
a 0 [3 dup] urtexlabel
<tex>
$B$
</tex>
0 b [3 dup] dltexlabel
<tex>
$M$
</tex>
M [3 dup] urtexlabel
<tex>
$N$
</tex>
N [3 dup] urtexlabel
<tex>
$\theta$
</tex>
M P milieu O milieu O milieu [3 dup] urtexlabel


O N (-) line
pointilles
P N (-) line

continu
/arrowangle -5 store
1 0 O N 0.2 (->) tripointarc 

vert
/I {a t Cos div 0} def
M I droite
N I droite
noir
O N I angledroit
(I) I urtext