Présentation de 317.jps

%% auteur : gh

%%conique_hyperbole.jps

600 setwidth
1000 setheight
-1.5 1.5 setxrange
-2.5 2.5 setyrange

/O {0 0} def
/a 0.6 def
/b 1 def
/c {a 2 exp b 2 exp add 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 {cosh a mul} def
/X2 {cosh a mul neg} def
/Y {sinh b mul} def

traceaxes
axesarrow

6 setlinewidth
rouge
-4 4 settrange
{X} {Y} courbeparam
{X2} {Y} courbeparam

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

noir
<tex>
$$a$$
</tex>
a 0 [3 dup] urtexlabel
<tex>
$$b$$
</tex>
0 b [3 dup] urtexlabel
<tex>
$$c$$
</tex>
F' [3 dup] uctexlabel
<tex>
$$-c$$
</tex>
F [3 dup] uctexlabel

<tex> 
$$
-{a^2 \over c}
$$ 
</tex> 
Dx  [2 dup] dltexlabel 

<tex> 
$$
{a^2 \over c}
$$ 
</tex> 
Dx'  [2 dup] drtexlabel 

vert
O a b droite
O a b neg droite

<tex> 
$$
y={b \over a} x
$$ 
</tex> 
O a 2 mul b 2 mul addv  [3 dup] ultexlabel 
<tex> 
$$
y=-{b \over a} x
$$ 
</tex> 
O a 2 mul neg b 2 mul addv  [3 dup] urtexlabel