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[1]+M1[2]*M3[1]*M4[1]+M2[1]*M3[1]*M4[2]-M2[2]*M3[1]*M4[1])/(M1[1]*M2[2 ]-M1[1]*M4[2]-M1[2]*M2[1]+M1[2]*M4[1]+M2[1]*M3[2]-M2[2]*M3[1]+M3[1]*M4 [2]-M3[2]*M4[1]), (M1[1]*M2[2]*M3[2]-M1[1]*M3[2]*M4[2]-M1[2]*M2[1]*M4[ 2]-M1[2]*M2[2]*M3[1]+M1[2]*M2[2]*M4[1]+M1[2]*M3[1]*M4[2]+M2[1]*M3[2]*M 4[2]-M2[2]*M3[2]*M4[1])/(M1[1]*M2[2]-M1[1]*M4[2]-M1[2]*M2[1]+M1[2]*M4[ 1]+M2[1]*M3[2]-M2[2]*M3[1]+M3[1]*M4[2]-M3[2]*M4[1])]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "r1:=-2*c*cos(t)+2*sqrt(b^2-c^2*sin (t)^2):\nr2:=-2*c*cos(t)-2*sqrt(b^2-c^2*sin(t)^2):\nrr1:=2*c*cos(t)+2* sqrt(a^2-c^2*sin(t)^2):\nrr2:=2*c*cos(t)-2*sqrt(a^2-c^2*sin(t)^2):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "F:=[c,0]:FF:=[-c,0]:N1:=[- c+rr1*cos(t),rr1*sin(t)];N2:=[-c+rr2*cos(t),rr2*sin(t)];NN1:=[c+r1*cos (t),r1*sin(t)];NN2:=[c+r2*cos(t),r2*sin(t)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#N1G7$,&%\"cG!\"\"*&,&*(\"\"#\"\"\"F'F--%$cosG6#%\"tG F-F-*&F,F-,&*$)%\"aGF,F-F-*&)F'F,F-)-%$sinGF0F,F-F(#F-F,F-F-F.F-F-*&F* F-F:F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#N2G7$,&%\"cG!\"\"*&,&*(\" \"#\"\"\"F'F--%$cosG6#%\"tGF-F-*&F,F-,&*$)%\"aGF,F-F-*&)F'F,F-)-%$sinG F0F,F-F(#F-F,F(F-F.F-F-*&F*F-F:F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$NN1G7$,&%\"cG\"\"\"*&,&*(\"\"#F(F'F(-%$cosG6#%\"tGF(!\"\"*&F,F(,&*$) %\"bGF,F(F(*&)F'F,F()-%$sinGF/F,F(F1#F(F,F(F(F-F(F(*&F*F(F:F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$NN2G7$,&%\"cG\"\"\"*&,&*(\"\"#F(F'F (-%$cosG6#%\"tGF(!\"\"*&F,F(,&*$)%\"bGF,F(F(*&)F'F,F()-%$sinGF/F,F(F1# F(F,F1F(F-F(F(*&F*F(F:F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "M11:=simplify(inters(F,NN1,N1,FF)):M12:=simplify(inters(F,NN1,N2, FF)):M21:=simplify(inters(F,NN2,N1,FF)):M22:=simplify(inters(F,NN2,N2, FF)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "BB:=numer(simplify (M12));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#BBG7$,0*(\"\"#\"\"\")-%$ cosG6#%\"tG\"\"$F))%\"cGF(F)!\"\"**F(F),(*&F0F))F+F(F)F)*$)%\"bGF(F)F) *$F0F)F2#F)F(F6F)F1F)F)**F(F),(F5F)*$)%\"aGF(F)F)F:F2F;F6F)F1F)F)**F(F )F4F;F=F;F+F)F2*(F(F)F+F)F0F)F)*&F4F;F1F)F2*&F=F;F1F)F2,$*(F(F)-%$sinG F-F),*F5F)*(F4F;F+F)F1F)F2*(F=F;F+F)F1F)F2*&F4F;F=F;F)F)F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "AAA:=c^2*sin(2*t)*sin(t)+c*((c^2*c os(t)^2+b^2-c^2)^(1/2)+(c^2*cos(t)^2+a^2-c^2)^(1/2))*cos(2*t)-2*(c^2*c os(t)^2+b^2-c^2)^(1/2)*(c^2*cos(t)^2+a^2-c^2)^(1/2)*cos(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$AAAG,(*()%\"cG\"\"#\"\"\"-%$sinG6#,$*&F)F *%\"tGF*F*F*-F,6#F0F*F**(F(F*,&*$,(*&F'F*)-%$cosGF2F)F*F**$)%\"bGF)F*F **$F'F*!\"\"#F*F)F**$,(F7F**$)%\"aGF)F*F*F>F?F@F*F*-F:F-F*F***F)F*F6F@ FBF@F9F*F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "BB[1];" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,0*(\"\"#\"\"\")-%$cosG6#%\"tG\"\"$F&) %\"cGF%F&!\"\"**F%F&,(*&F-F&)F(F%F&F&*$)%\"bGF%F&F&*$F-F&F/#F&F%F3F&F. F&F&**F%F&,(F2F&*$)%\"aGF%F&F&F7F/F8F3F&F.F&F&**F%F&F1F8F:F8F(F&F/*(F% F&F(F&F-F&F&*&F1F8F.F&F/*&F:F8F.F&F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(BB[1]-AAA);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "B:=numer(simpli fy(M11));simplify(subs(b=a,M11));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#> %\"BG7$,0*(\"\"#\"\"\")-%$cosG6#%\"tG\"\"$F))%\"cGF(F)!\"\"**F(F),(*&F 0F))F+F(F)F)*$)%\"bGF(F)F)*$F0F)F2#F)F(F6F)F1F)F)**F(F),(F5F)*$)%\"aGF (F)F)F:F2F;F6F)F1F)F2**F(F)F4F;F=F;F+F)F)*(F(F)F+F)F0F)F)*&F4F;F1F)F2* &F=F;F1F)F),$*(F(F)-%$sinGF-F),*F5F2*(F4F;F+F)F1F)F)*(F=F;F+F)F1F)F2*& F4F;F=F;F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$*(-%$cosG6#%\"tG\" \"\"%\"aG\"\"#,(*&)%\"cGF+F))F%F+F)F)*$)F*F+F)F)*$F.F)!\"\"#F4F+*(-%$s inGF'F),&*$F2F)F)*$F.F)F4F)F,F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "r1:=(a^2-c^2+c^2*cos(t)^2)^(1/2):r2:=(b^2-c^2+c^2*cos(t)^2)^(1 /2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "A:=c^2*sin(2*t)*sin (t)+c*(r2-r1)*cos(2*t)+2*r1*r2*cos(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG,(*()%\"cG\"\"#\"\"\"-%$sinG6#,$*&F)F*%\"tGF*F*F*-F,6#F0F* F**(F(F*,&*$,(*&F'F*)-%$cosGF2F)F*F**$)%\"bGF)F*F**$F'F*!\"\"#F*F)F**$ ,(F7F**$)%\"aGF)F*F*F>F?F@F?F*-F:F-F*F***F)F*F6F@FBF@F9F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "AA:=2*sin(t)*(-c^2*cos(t)^2 +((c^2*cos(t)^2+b^2-c^2)^(1/2)-(c^2*cos(t)^2+a^2-c^2)^(1/2))*c*cos(t)+ (c^2*cos(t)^2+b^2-c^2)^(1/2)*(c^2*cos(t)^2+a^2-c^2)^(1/2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AAG,$*(\"\"#\"\"\"-%$sinG6#%\"tGF(,(*&)% \"cGF'F()-%$cosGF+F'F(!\"\"*(,&*$,(F.F(*$)%\"bGF'F(F(*$F/F(F4#F(F'F(*$ ,(F.F(*$)%\"aGF'F(F(F " 0 "" {MPLTEXT 1 0 35 "simplify(A-B[1]);simplify(AA-B[2]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "M11 :=[A/(r1+r2),AA/(r1+r2)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simplify(subs(b=a,M11));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$*(-% $cosG6#%\"tG\"\"\"%\"aG\"\"#,(*&)%\"cGF+F))F%F+F)F)*$)F*F+F)F)*$F.F)! \"\"#F4F+*(-%$sinGF'F),&*$F2F)F)*$F.F)F4F)F,F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "ca fait l'ellipse x^2/a^2 +y^2/(a^2-c^2) = 1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "c,a,b:=8,1,2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "c,a,b:=1,3/2,3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "c,a,b:=1,1.5,1.9:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "courbe11:=plot([op(M11),t=0..2*Pi],color=red):c ourbe12:=plot([op(M12),t=0..2*Pi],color=red):courbe21:=plot([op(M21),t =0..2*Pi]):courbe22:=plot([op(M22),t=0..2*Pi]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 80 "C:=plot([op(N1),t=0..2*Pi],color=blue):CC:=plo t([op(NN1),t=0..2*Pi],color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "display(courbe11,courbe12);" }}{PARA 13 "" 1 "" {GLPLOT2D 575 575 575 {PLOTDATA 2 "6&-%'CURVESG6$X4%)anythingG6\"6\"[g l'\"%!!!#[dl\"cw\"#!!!!!!!!4002AAAAAAAAAAAB4002A75B1585966840029F16CAF 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