%% auteur : gh
%% conique_ellipse_tangente_2.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
0 pi 2 mul settrange
{X} {Y} courbeparam

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

noir
<tex>
$$M$$
</tex>
M [3 dup] urtexlabel
<tex>
$$N$$
</tex>
N [3 dup] urtexlabel
[F F'] points
<tex>
$$F$$
</tex>
F [3 dup] dctexlabel
<tex>
$$F'$$
</tex>
F' [3 dup] dctexlabel


vert
/I {a t Cos div 0} def
M I droite
/v {t Sin b mul
     a t Cos div a t Cos mul sub} def
/P {M v subv} def
M P droite

bleu
F M (-) line
F' M (-) line
0.7 setlinewidth
/arrowangle -5 store
F M P 0.2 (-) tripointarc 
P M F' 0.2 (=) tripointarc