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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "restart:with(plo
ts):" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {TEXT 203 49 "Warning, \+
the name changecoords has been redefined" }{TEXT 203 0 "" }}}{EXCHG 
{PARA 202 "" 0 "" {TEXT 204 10 "EXERCICE 5" }{TEXT 205 0 "" }}}{SECT 
1 {PARA 203 "" 0 "" {TEXT -1 0 "" }}{PARA 204 "" 0 "" {TEXT 205 0 "" }
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 69 "racines:=proc(P,X)  #P \+
est une expression polynomiale de degr\351 2 en X" }{MPLTEXT 1 202 0 "
" }{MPLTEXT 1 202 21 "\nlocal a,b,c,d,r1,r2;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 66 "\nc:=subs(X=0,P):b:=subs(X=0,diff(P,X)):a:=subs(X=0
,diff(P,X$2))/2:" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n#P(X)=aX^
2+bX+c" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 42 "\nd:=b^2-4*a*c: #d es
t le discriminant de P" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 129 "\nif
 is(d>=0) then r1:=(-b-sqrt(d))/(2*a): r2:=(-b+sqrt(d))/(2*a); else r1
:=(-b- I*sqrt(-d))/(2*a): r2:=(-b+I*sqrt(-d))/(2*a); fi;" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 43 "\nif is(a>0) then [r1,r2]; else [r2,r1]; \+
fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 
0 "" }{MPLTEXT 1 202 1 "\n" }}}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 
202 38 "a:=5:b:=3:F:=(x,y)->x^2/a^2+y^2/b^2-1;" }{MPLTEXT 1 202 0 "" }
}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"FG6\"f*6$I\"xGF%I\"yGF%F%6$I)ope
ratorGF%I&arrowGF%F%,(*&9$\"\"#I\"aGF%!\"#\"\"\"*&9%F0I\"bGF%F2F3!\"\"
F3F%F%F%" }{TEXT 206 0 "" }}}{SECT 1 {PARA 203 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 99 "vec_normal:=proc(F,M)  \+
      #fonction d\351finissant la conique et M point o\371 l'on calcul
e la normale" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 17 "\nlocal u,n,nor
me;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 36 "\nu:=[diff(F(x,y),x),dif
f(F(x,y),y)];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 26 "\nn:=subs(x=M[
1],y=M[2],u);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 60 "\nnorme:=sqrt(
n[1]^2+n[2]^2):  #Calcule la norme du vecteur n" }{MPLTEXT 1 202 0 "" 
}{MPLTEXT 1 202 51 "\nn:=[n[1]/norme,n[2]/norme]:  #normalise le vecte
ur" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 
"" }{MPLTEXT 1 202 1 "\n" }}}}{EXCHG {PARA 205 "" 1 "" {TEXT 206 0 "" 
}}}{SECT 1 {PARA 203 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 200 "> " 0 "
" {MPLTEXT 1 202 25 "impact_ellipse:=proc(M,d)" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 24 "\nlocal r,t,n,ps,P,delta;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 42 "\nr:=racines(F(M[1]+t*d[1],M[2]+t*d[2]),t);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 36 "\nP:=[M[1]+r[2]*d[1],M[2]+r[2]
*d[2]];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\nn:=vec_normal(F,P)
:ps:=d[1]*n[1]+d[2]*n[2]:" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n
delta:=[d[1]-2*ps*n[1],d[2]-2*ps*n[2]];" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 11 "\n[P,delta];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 
5 "\nend:" }{MPLTEXT 1 202 0 "" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 21 "P:=[0,0];theta:=Pi
/4;" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"PG6\"
7$\"\"!F'" }{TEXT 206 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I&theta
G6\",$I#PiGI*protectedGF(#\"\"\"\"\"%" }{TEXT 206 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 51 "d:=[cos(theta),sin(theta)]:trajet:=P:#d:=[4/5,3/5];
" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 
20 "for i from 1 to 5 do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\n \+
Imp:=impact_ellipse(P,d);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n
P:=Imp[1]:d:=Imp[2]:trajet:=trajet,P;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 
1 202 4 "\nod:" }{MPLTEXT 1 202 0 "" }}{PARA 206 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 7 "trajet;" }
{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6(7$\"\"!F$7$,$*&
\"#<#\"\"\"\"\"#F+F)#\"#:\"#MF&7$,$F'#\"(l3B$\"(1^>',$F'#!(&4IDF37$,$F
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G3'\"C%>ST4:i.[ui#[(yy/1\",$F'#!B&pra-!*\\`xx1fp^qbSFC7$,$F'#\"W:g<xd)
pi'))QZL:24g$['oav,m()y\"o\"\"WM;/I8m%G$)zMh.\\<;e%)QBBt^mDQv),$F'#\"W
N\"4T)[p+06ZfKRp&eawOMdTB&)4$*Q%FK" }{TEXT 206 0 "" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 45 "Boule:=plot([trajet],style=line,thickness=2):" }
{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 59 "B
illard:=implicitplot(F(x,y)=0,x=-5..5,y=-5..5,color=blue):" }{MPLTEXT 
1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}
{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 26 "display(\{Boule, Billard
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