%% 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 $$F$$ F [3 dup] dctexlabel $$F'$$ F' [3 dup] dctexlabel $$D$$ Dx 0 1.5 subv [3 dup] urtexlabel $$D'$$ Dx' 0 1.5 subv [3 dup] urtexlabel noir $$a$$ a 0 [3 dup] urtexlabel $$b$$ 0 b [3 dup] urtexlabel $$c$$ F' [3 dup] uctexlabel $$-c$$ F [3 dup] uctexlabel $$ -{a^2 \over c} $$ Dx [2 dup] dltexlabel $$ {a^2 \over c} $$ Dx' [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 [3 dup] ultexlabel $$ y=-{b \over a} x $$ O a 2 mul neg b 2 mul addv [3 dup] urtexlabel