{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 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 }{PSTYLE "Warning" -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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "eliminate(\{T=P*sin( x)/sin(f+x),sin(f+b)=k*sin(f),sin(b-x)=k*sin(x)\},\{x,f\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$<$/%\"xG-%'arctanG6#*&-%$sinG6#%\"bG\"\"\" ,&-%$cosGF-F/%\"kGF/!\"\"/%\"fG-F(6$**%\"PGF/F+F/%\"TGF4F3F4**F:F/F;F4 F3F4,&F1F4F3F/F/<#*&)F+\"\"#F/,***FAF/)F:FAF/F1F/F3F/F4*&FDF/)F3FAF/F/ *(\"\"%F/)F;FAF/FFF/F4*$FDF/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "solve(-2*P^2*cos(b)*k+P^2*k^2-4*T^2*k^2+P^2,T);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&#\"\"\"\"\"#F&*(,(*(F'F&-%$cosG6#% \"bGF&%\"kGF&!\"\"*$)F/F'F&F&F&F&F%%\"PGF&F/F0F&F&,$*&#F&F'F&F(F&F0" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solve(1/2*(-2*cos(b)*k+k^2 +1)^(1/2)*P/k=Q*cos(t),cos(b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* &#\"\"\"\"\"#F&*(,(*&)%\"PGF'F&)%\"kGF'F&F&*$F+F&F&**\"\"%F&)%\"QGF'F& )-%$cosG6#%\"tGF'F&F-F&!\"\"F&F,!\"#F.F9F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solve(1/2*(-2*cos(b)*k+k^2+1)^(1/2)*P/k=Q*cos(t) ,cos(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&**,(*(F 'F&-%$cosG6#%\"bGF&%\"kGF&!\"\"*$)F/F'F&F&F&F&F%%\"PGF&%\"QGF0F/F0F&F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$COSG,$*&#\"\"\"\"\"#F(*(*&,(*(F)F(-%$cosG6#%\"tGF(% \"aGF(!\"\"F(F(*$)F2F)F(F(F(F2!\"#F'%\"pGF(F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SIN G,$*&#\"\"\"\"\"#F(*$,&\"\"%F(*&,(*(F)F(-%$cosG6#%\"tGF(%\"aGF(!\"\"F( F(*$)F4F)F(F(F()%\"pGF)F(F5F'F(F(" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "simplify(1+k^2-2*k*(1/2*(P^2*k^2+P^2-4*Q^2*cos(t)^2*k^2)/P^2/k)); " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "A:=[0,0]:B:=[-a*sin(t),a* cos(t)]:COS:=simplify(subs(k=1/a,b=t,P=p*Q,1/2*(-2*cos(b)*k+k^2+1)^(1/ 2)*P/Q/k));SIN:=sqrt(1-COS^2);C:=[0,1]:rho:=L-2/p*COS;rho2:=L+2/p*COS; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$COSG,$*&#\"\"\"\"\"#F(*(*&,(*(F )F(%\"aGF(-%$cosG6#%\"tGF(!\"\"F(F(*$)F.F)F(F(F(F.!\"#F'%\"pGF(F.F(F(F (" }}{PARA 11 "" 1 "" {XPPMATH 20 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