{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Andale Mono" 1 14 0 0 1 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 0 0 0 255 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "moi" -1 256 "Times" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Century Schoolbook" 1 10 0 128 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "War ning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Century \+ Schoolbook" 1 12 0 0 1 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Century Schoolbook " 1 10 0 128 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Lucida Sans" 1 12 0 0 255 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Fo nt 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 938 "focale:=proc(a,b,aa )\nlocal A,B,C,d,sol,x:\nP:=expand(b^4*sin(aa)^2-4*x*(x-2*a)*(x^2-2*a* x+b^2*cos(aa))):\nA:=2*a:B:=b^2*cos(aa):C:=b^2*sin(aa):sol:=[solve(P,x )]:\nsol:=map(evalf,sol):\nk:=1:while k <= nops(sol) do if Im(sol[k])< >0 then sol:=subsop(k=NULL,sol) else k:=k+1 fi od;\nsol:=sort(sol):\nd :=evalf(a-b*cos(aa/2)):\nif d>=0 and a>0 then \novale:=plot([(-C-sqrt (P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=sol[1]..sol[2],color=red):\nbi1:= plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=sol[3]..2*a,y=-4..4 ,discont=false,color=red):\nbi2:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P ))/(x-A)/2],x=2*a..sol[4],y=-4..4,discont=false,color=red):\ndisplay(o vale,bi1,bi2,thickness=2)\n \nelse s1:=min(sol[1],sol[2]):s2:=max(sol[ 1],sol[2]):\nbi1:=plot([[x,(-C-sqrt(P))/(x-A)/2,x=s1..2],[x,(-C+sqrt(P ))/(x-A)/2,x=s1..2*a]],color=red):\nbi2:=plot([[x,(-C-sqrt(P))/(x-A)/2 ,x=2..s2],[x,(-C+sqrt(P))/(x-A)/2,x=2*a..s2]],color=red):\ndisplay(bi1 ,bi2,thickness=2) \nfi\nend:" }}{PARA 7 "" 1 "" {TEXT -1 64 "Warning, \+ `P` is implicitly declared local to procedure `focale`\n" }}{PARA 7 " " 1 "" {TEXT -1 64 "Warning, `k` is implicitly declared local to proce dure `focale`\n" }}{PARA 7 "" 1 "" {TEXT -1 68 "Warning, `ovale` is im plicitly declared local to procedure `focale`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `bi1` is implicitly declared local to procedure \+ `focale`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `bi2` is implicitl y declared local to procedure `focale`\n" }}{PARA 7 "" 1 "" {TEXT -1 65 "Warning, `s1` is implicitly declared local to procedure `focale`\n " }}{PARA 7 "" 1 "" {TEXT -1 65 "Warning, `s2` is implicitly declared \+ local to procedure `focale`\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 366 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{XPPMATH 20 "6#>%$solG7&$\"+++++?!\"*$\"\"!F*^$$ \"\"\"F*$\"+&pvDe%!#5^$F,$!+&pvDe%F0" }}{PARA 8 "" 1 "" {TEXT -1 52 "E rror, (in cot) numeric exception: division by zero\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$!\"\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$ $\"\"\"\"\"!$!+&pvDe%!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1441 "if d>0 then sol:=sort(sol):\novale:=plot([(-C-sqrt(P))/(x-A)/2,( -C+sqrt(P))/(x-A)/2],x=sol[1]..sol[2],scaling=constrained,color=red): \nbi1:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=sol[3]..2,y= -4..4,scaling=constrained,discont=false,color=red):\nbi2:=plot([(-C-sq rt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=2..sol[4],y=-4..4,discont=false ,color=red):\nas:=plot([[[1,-4],[1,4]],[[2,-4],[2,4]]],color=black,lin estyle=[4,1]):\nF:=[0,0]:S:=[2*a,-2*a*cot(aa)]:OO:=[a,a*tan(aa/2)]:\nd roites:=display(plot([[(1-t)*F[1]+t*S[1],(1-t)*F[2]+t*S[2],t=-1..2],[( 1-t)*F[1]+t*OO[1],(1-t)*F[2]+t*OO[2],t=0..2],[(1-t)*OO[1]+t*S[1],(1-t) *OO[2]+t*S[2],t=-1..2],[t,2*t,t=0..5]],color=black,linestyle=[1,1,1,2] ,numpoints=2)):\nprint(display(ovale,bi1,bi2,as,droites,axes=none))\n \n\n \nelse s1:=min(sol[1],sol[2]):s2:=max(sol[1],sol[2]):\nbi1:=plot( [(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=s1..2,y=-4..4,scaling=co nstrained,discont=false,color=red):\nbi2:=plot([(-C-sqrt(P))/(x-A)/2,( -C+sqrt(P))/(x-A)/2],x=2..s2,y=-4..4,scaling=constrained,discont=false ,color=red):\nas:=plot([[[1,-4],[1,4]],[[2,-4],[2,4]]],color=black,lin estyle=[4,1]):\nF:=[0,0]:S:=[2*a,-2*a*cot(aa)]:OO:=[a,a*tan(aa/2)]:\nd roites:=display(plot([[(1-t)*F[1]+t*S[1],(1-t)*F[2]+t*S[2],t=-1..2],[( 1-t)*F[1]+t*OO[1],(1-t)*F[2]+t*OO[2],t=0..2],[(1-t)*OO[1]+t*S[1],(1-t) *OO[2]+t*S[2],t=-1..2],[t,2*t,t=0..5]],color=black,linestyle=[1,1,1,2] ,numpoints=2)):\nprint(display(bi1,bi2,as,droites,axes=none)) \nfi:" } }{PARA 8 "" 1 "" {TEXT -1 52 "Error, (in cot) numeric exception: divis ion by zero\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "restart:P :=expand(b^4*sin(aa)^2-4*x*(x-2*a)*(x^2-2*a*x+b^2*cos(aa))):A:=2*a:B:= b^2*cos(aa):C:=b^2*sin(aa):sol:=[solve(P,x)]:aa:=Pi/3.5:aa:=2*arccos(a /b)+0.2:aa:=0.001:" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "a:=1:b:=0.9:sol:=map(evalf,s ol);evalf(2*cot(aa)):d:=evalf(a-b*cos(aa/2));sol[4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG7&$\"+,,++?!\"*$!$,\"F($\"+F,*eV\"F($\"+M()4T c!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$\"+D6++5!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+M()4Tc!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1213 "if d>0 then sol:=sort(sol):\novale:=plot([(-C-sqrt( P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=sol[1]..sol[2],scaling=constrained ,color=red):\nbi1:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x= sol[3]..2,y=-4..4,scaling=constrained,discont=false,color=red):\nbi2:= plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=2..sol[4],y=-4..4,d iscont=false,color=red):\nas:=plot([[[1,-4],[1,4]],[[2,-4],[2,4]]],col or=black,linestyle=[4,1]):\nF:=[0,0]:S:=[2*a,-2*a*cot(aa)]:OO:=[a,a*ta n(aa/2)]:\ndroites:=display(plot([[t,t/2,t=0..5],[0,t,t=-3..3],[t,0,t= 0..2]],color=black,linestyle=[1,1,1,2],numpoints=2)):\nprint(display(o vale,bi1,bi2,as,droites,axes=none))\n\n\n \nelse s1:=min(sol[1],sol[2] ):s2:=max(sol[1],sol[2]):\nbi1:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P) )/(x-A)/2],x=s1..2,y=-4..4,scaling=constrained,discont=false,color=red ):\nbi2:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=2..s2,y=-4 ..4,scaling=constrained,discont=false,color=red):\nas:=plot([[[1,-4],[ 1,4]],[[2,-4],[2,4]]],color=black,linestyle=[4,1]):\nF:=[0,0]:S:=[2*a, -2*a*cot(aa)]:OO:=[a,a*tan(aa/2)]:\ndroites:=display(plot([[t,t/2,t=0. .5],[0,t,t=-3..3],[t,0,t=0..2]],color=black,linestyle=[1,1,1,2],numpoi nts=2)):\nprint(display(bi1,bi2,as,droites,axes=none)) \nfi:" }}{PARA 13 "" 1 "" {GLPLOT2D 692 617 617 {PLOTDATA 2 "61-%'CURVESG6$7]o7$$!30+ +++++55!#C$\"3z)z0'*))>c7#!#@7$$\"3U+++]])Ro(F-$\"3InjPu)GJy\"!#>7$$\" 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ALIC,12])):\nprinc:=display(pointplot([2*a,-2*a*cot(aa)],symbol=circle ),textplot([2*a-0.2,-2*a*cot(aa),'S'],color=black,font=[TIMES,ITALIC,1 2])):\nprint(display(ovale,bi1,bi2,as,foyer,centre,princ,xtickmarks=0, ytickmarks=0))\n\n\n \nelse s1:=min(sol[1],sol[2]):s2:=max(sol[1],sol[ 2]):\nbi1:=plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=s1..2,y= -4..4,scaling=constrained,discont=false,color=red,thickness=2):\nbi2:= plot([(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2],x=2..s2,y=-4..4,scali ng=constrained,discont=false,color=red,thickness=2):\nas:=plot([[[1,-4 ],[1,4]],[[2,-4],[2,4]]],color=[black,green],linestyle=[4,1]):\nfoyer: =display(pointplot([0,0],symbol=circle),textplot([0.2,-0.3,'F'],color= black,font=[TIMES,ITALIC,12])):\ncentre:=display(pointplot([a,a*tan(aa /2)],symbol=circle),textplot([a+0.3,a*tan(aa/2),'O'],color=black,font= [TIMES,ITALIC,12])):\nprinc:=display(pointplot([2*a,-2*a*cot(aa)],symb ol=circle),textplot([2*a-0.2,-2*a*cot(aa),'S'],color=black,font=[TIMES 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(x-A)/2,x=sol[3]..2]],discont=false,color=red,thickness=2):\nbi2:=plot ([x,(-C-sqrt(P))/(x-A)/2,(-C+sqrt(P))/(x-A)/2,x=2..sol[4]],discont=fal se,color=red,thickness=2):\nprint(display(ovale,bi1,bi2,as,foyer,centr e,cercles,princ,axes=none,view=[-1..3,-2..2]))\n\nelse s1:=min(sol[1], sol[2]):s2:=max(sol[1],sol[2]):\nbi1:=plot([[x,(-C-sqrt(P))/(x-A)/2,x= s1..2],[x,(-C+sqrt(P))/(x-A)/2,x=s1..2]],scaling=constrained,discont=f alse,color=red,thickness=2):\nbi2:=plot([[x,(-C-sqrt(P))/(x-A)/2,x=2.. s2],[x,(-C+sqrt(P))/(x-A)/2,x=2..s2]],scaling=constrained,discont=fals e,color=red,thickness=2):\nas:=plot([[[1,-4],[1,4]],[[2,-4],[2,4]]],co lor=[black,green],linestyle=[4,1]):\nprint(display(bi1,bi2,as,foyer,ce ntre,cercles,princ,axes=none,view=[-1..3,-1.5..1.5])) \nfi:" }}{PARA 13 "" 1 "" {GLPLOT2D 543 554 554 {PLOTDATA 2 "6<-%'CURVESG6%7ip7$$!3-+ ++++++5!#?$\"3#4l*)=GvbB#!#>7$$\"3\"*******fH.IO!#@$\"3i1Gl=L`Z[F-7$$ \"3++++#f1gs\"F*$\"3wbG`LyeEfF-7$$\"39+++)))4!*3$F*$\"35TT%f6aBv'F-7$$ 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