%% auteur : gh 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 5 setlinewidth rouge O a 0 (-) line O 0 b (-) line a 0 0 b (-) line a 0 O 0 b angledroit 2 setlinewidth /dy {0 0.1} def /dx {0.1 0} def O dy subv a 0 dy subv (<->) line O dx subv 0 b dx subv (<->) line 0 b dx dy addv addv a 0 dx dy addv addv (<->) line $$c$$ a 0 0 b milieu [2 dup] urtexlabel $$b$$ O 0 b milieu [2 dup] cltexlabel $$a$$ a 0 O milieu [2 dup] drtexlabel noir 3 setlinewidth vert -4 4 settrange {X} {Y} courbeparam {X2} {Y} courbeparam 3 setlinewidth continu bleu [F F'] points D droite D' droite $$F$$ F [2 dup] dctexlabel $$F'$$ F' [2 dup] dctexlabel $$D$$ Dx 0 1.5 subv [2 dup] drtexlabel $$D'$$ Dx' 0 1.5 subv [2 dup] drtexlabel vert O a b droite O a b neg droite $$ y={b \over a} x $$ O a 2 mul b 2 mul addv [2 dup] ultexlabel $$ y=-{b \over a} x $$ O a 2 mul neg b 2 mul addv [2 dup] urtexlabel