%% PhS
%%

35 setxunit
-8 12  setxrange
-6.5 6.5 setyrange



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% procédures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/bddroite {
8 dict begin
	/kd exch def
	/kg exch def
	/By exch def
	/Bx exch def
	/B {Bx By} def
	/Ay exch def
	/Ax exch def
	/A {Ax Ay} def
	gsave
	[A A B vecteur kg mulv addv A A B vecteur kd mulv addv] ligne
	grestore
end
	} def



/Fleche_sur_C {
2 dict begin  %% t long
	/long exch def
	/t exch def
	[t xdet t ydet dupp dupp 
	t 0.01 add dup xdet exch ydet vecteur
	%% 0.01 1 exch div mulv
	0.01 -1 exch div mulv %% ici, il faut tricher...j'ai honte!
	dupp norme long exch div mulv addv]
	(->) ligne
end
	} def

/Fleche_sur_Cp {
2 dict begin  %% t long
	/long exch def
	/t exch def
	[t xdet neg t ydet dupp dupp 
	t 0.01 add dup xdet neg exch ydet vecteur
	%% 0.01 1 exch div mulv
	0.01 -1 exch div mulv %% ici, il faut tricher...j'ai honte!
	dupp norme long exch div mulv addv]
	(->) ligne
end
	} def




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% definition des points
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/a {3} def
/c {3.8} def
/b {c c mul a a mul sub sqrt} def
/e {c a div} def
/Kx {a e div} def
/K {Kx neg 0} def
/K+ {K 0 6 addv} def
/K- {K 0 -6 addv} def
/Kp {Kx 0} def
/Kp+ {Kp 0 6 addv} def
/Kp- {Kp 0 -6 addv} def
/O {0 0} def
/F {c neg 0} def
/Fp {c 0} def
/S1 {a neg 0} def
/S2 {a 0} def
/B {0 b} def


/R11 {a neg b} def
/R12 {a b} def
/R21 {a neg b neg} def
/R22 {a b neg} def
/omeg {F O milieu} def
/Ry {1 e e mul 1 exch div sub sqrt a mul} def
/R {Kx neg Ry} def



/xdet {settvar t t mul b b mul div 1 add sqrt a mul} def
/ydet {settvar t} def


/Mx {b 1.3 mul xdet} def
/My {b 1.3 mul ydet} def
/M {Mx My} def
/H {M Kp Kp+ orthoproj} def




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% definition d'une couleur
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/coul1 {120 255 div 70 255 div 9 255 div setrgbcolor} def




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% tracés
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.1 setlinewidth
[O F Fp S1 S2 B K Kp M] points
F Fp -0.6 2 bddroite
[O 0 -6.5 addv O 0 6.5 addv] ligne

coul1
2 setlinewidth
b -2.7 mul b 2.7 mul settrange
{xdet} {ydet} courbeparam
b -2.2 mul b 2.2 mul settrange
{xdet neg} {ydet} courbeparam

/arrowscale {2.5 dup} def


5 0.2 Fleche_sur_C
4 0.2 Fleche_sur_Cp
-5 0.2 Fleche_sur_C
-4 0.2 Fleche_sur_Cp




1.1 setlinewidth
vert
[K+ K-] ligne
[Kp+ Kp-] ligne


rouge
[Fp M] ligne
/arrowangle -9 def
Fp 1 0 addv Fp M 1.3 (->) tripointarc
/arrowangle 0 def



bleu
pointilles
[R11 R12 R22 R21] polygone
noir
mixte
0.6 setlinewidth
R11 R22 -1 2 bddroite
R12 R21 -1 2 bddroite

orange
pointilles
Fp Fp a b addv -0.2 2.5 bddroite
Fp Fp a neg b addv -2 0.2 bddroite


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% texte
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

setTimesItalic
noir
  (O) O [1.8 dup] dltext
  (F) Fp [1.8 dup] drtext
  (B) B [1.5 dup] ultext

  (M) M  [1.5 dup] crtext

vert
  (K) Kp [1.5 dup] dltext

<latex>
$ \mathcal{D}' $
</latex>
 K 0 -5 addv [2 dup] cltexlabel

<latex>
$ \mathcal{D} $
</latex>
 Kp 0 -5 addv[2 dup] crtexlabel



rouge
<latex>
$ \theta $
</latex>
 Fp 1.6 0.5 addv [2 dup] cctexlabel

<latex>
$ \theta=0 $
</latex>
b neg 0 -0.7 0 addv [1.5 dup] dltexlabel


orange
<latex>
$ \theta=\mathrm{Arccos}(\frac{1}{e}) $
</latex>
9.4 2.8 [1.5 dup] cctexlabel

<latex>
$ \theta=-\mathrm{Arccos}(\frac{1}{e}) $
</latex>
10.5 -5 [1.5 dup] cctexlabel

noir
<latex>
\fbox{$ \rho(\theta)=\displaystyle\frac{p}{1-e\cos(\theta)} $}
</latex>
9 -1.2 [1.8 dup] cctexlabel