// Macros :
$macros={};
$macros["Tgt1ptCnk"]={
	name:"Tgt 1 pt Cnk",
	parameters:["quadric","point"],
	exec:
	function (Quad,M){
B=DefinitionPoint("B",Quad,1);
P2=DefinitionPoint("P2",Quad,3);
P6=Point("P6","Quad.center()","0");
L1=Line("L1",P6,M);
Par1=Parallel("Par1",L1,B);
Par2=Parallel("Par2",L1,P2);
P4=OrderedIntersection("P4",Par1,Quad,1,B);
P5=OrderedIntersection("P5",Par2,Quad,0,P2);
M1=MidPoint("M1",P5,P2);
M2=MidPoint("M2",B,P4);
L2=Line("L2",M2,M1);
Par3=Parallel("Par3",L2,M);
STL(M,"c:#b40000;o:1;s:6;sn:true;f:30");
STL(Par3,"c:#780013;s:1;f:30;p:0");
return [M,Par3];
}};

// Coordinates System :
SetCoords(929.6298998894928,245.95541317586088,30.396374981499903);


// Geometry :
E14=Expression("E14","Dans le triangle OUV rectangle isoc\u00e8le en O, a son hypoth\u00e8nuse de longueur sqrt(2).","","","3","-29.5966180321513","-8.357726438720336");
O=Point("O",-7.345913697209723,-3.4313050009708768);
E5=Expression("E5","Illustration de l'existence de bases orthogonales : dans le rep\u00e8re (O,OI, OJ), u(x,y), v(x',y')","","","2","-29.5966180321513","7.104643672388483");
E6=Expression("E6","on consid\u00e8re le produit scalaire : (u,v)=xx'+yy'","","","3","-29.5966180321513","6.117683878062389");
E7=Expression("E7","En bleu clair la ligne de niveau - 'le cercle' - (u,u) = 1","","","2","-29.5966180321513","5.130724083736293");
E9=Expression("E9","U est un point de la conique (donc OU=1)","","","3","-29.5966180321513","4.143764289410199");
E10=Expression("E10","V est un point de la conique (OV=1) sur l'orthogonal de (OU)","","","3","-29.5966180321513","3.1568044950841037");
E13=Expression("E13","Soit M tel que vect(OM)=vect(UV). [OM) coupe la conique en K","","","3","-29.5966180321513","-5.067860457633354");
E12=Expression("E12","On peut v\u00e9rifier le th\u00e9or\u00e8me de Pythagore sur le vecteur UV","","","6","-29.5966180321513","-3.7519140651985605");
P14=Point("P14",-28.642556897636076,-0.4291494243007076);
I=Point("I",-0.9373939166759626,-2.289930695426519);
J=Point("J",-4.1397502450981225,3.706714286359465);
P7=Point("P7",-21.70928965024638,0.31805262864878103);
Symc3=Symmetry("Symc3",O,J);
M3=MidPoint("M3",O,I);
L2=Line("L2",O,J);
L1=Line("L1",O,I);
Symc2=Symmetry("Symc2",O,I);
M1=MidPoint("M1",O,I);
P1=Point("P1","O+(sqrt(3)/2)*(J-O)","0");
P2=Point("P2","M1+P1-O","0");
Symc1=Symmetry("Symc1",M1,P2);
Quad=Quadric("Quad",Symc2,Symc1,I,P2,J);
U=PointOn("U",Quad,[-0.5362764332588178,1.3450124994736676]);
P6=Point("P6","Quad.center()","0");
E11=Expression("E11","","","","Quad.foci()","-20.918025704739083","7.269136971442832");
R1=Ray("R1",O,U);
Par1=Parallel("Par1",L2,U);
S1=Segment("S1",O,U);
Par2=Parallel("Par2",L1,U);
Ux=OrderedIntersection("Ux",Par1,L1,0);
P3=OrderedIntersection("P3",R1,Quad,1);
Uy=OrderedIntersection("Uy",Par2,L2,0);
yU=ExpressionOn("yU","","","","(y(Uy)-y(O))/(y(J)-y(O))",P7,[20,10]);
S5=Segment("S5",U,Uy);
xU=ExpressionOn("xU","","","","(x(Ux)-x(O))/(x(I)-x(O))",P7,[20,-10]);
L11=Line("L11",P6,P3);
S6=Segment("S6",U,Ux);
E2=ExpressionOn("E2","(u,u) = ","","","xU*xU+yU*yU",P14,[20,-20]);
Par11=Parallel("Par11",L11,Symc1);
Par21=Parallel("Par21",L11,P2);
P4=OrderedIntersection("P4",Par11,Quad,1,Symc1);
P5=OrderedIntersection("P5",Par21,Quad,0,P2);
M2=MidPoint("M2",Symc1,P4);
M11=MidPoint("M11",P5,P2);
L21=Line("L21",M2,M11);
Par31=Parallel("Par31",L21,P3);
Par5=Parallel("Par5",Par31,O);
P15=OrderedIntersection("P15",Par5,Quad,1);
V=Point("V","[P15[0],P15[1]]","0");
Par3=Parallel("Par3",L2,V);
S9=Segment("S9",V,U);
S2=Segment("S2",O,V);
M=Point("M","O+V-U","0");
Par4=Parallel("Par4",L1,V);
R2=Ray("R2",O,M);
S4=Segment("S4",V,M);
Vy=OrderedIntersection("Vy",Par4,L2,0);
Vx=OrderedIntersection("Vx",Par3,L1,0);
S3=Segment("S3",O,M);
xV=ExpressionOn("xV","","","","(x(Vx)-x(O))/(x(I)-x(O))",P7,[140,-10]);
S8=Segment("S8",V,Vy);
K=OrderedIntersection("K",R2,Quad,1);
S7=Segment("S7",V,Vx);
yV=ExpressionOn("yV","","","","(y(Vy)-y(O))/(y(J)-y(O))",P7,[140,10]);
E4=Expression("E4","UV=OM= abscisse de M dans le rep\u00e8re (O,K) = d(O,M)/d(O,K) = ","","","d(O,M)/d(O,K)","-29.5966180321513","-6.7127934481768445");
E3=ExpressionOn("E3","(v,v) = ","","","xV*xV+yV*yV",P14,[20,10]);
E1=ExpressionOn("E1","(u,v) = xU*xV+yU*yV = ","","","xU*xV+yU*yV",P14,[20,40]);


// Styles :
STL(E14,"c:#966400;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(O,"c:#0000b2;o:1;s:6;sn:true;f:18");
STL(E5,"c:#0000b2;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E6,"c:#0000b2;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E7,"c:#2c69cf;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E9,"c:#966400;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E10,"c:#966400;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E13,"c:#007c7c;s:7;f:14;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E12,"c:#0000b2;s:7;f:14;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(P14,"c:#0000b2;s:4;f:30;sp:1");
STL(I,"c:#0000b2;o:1;s:6;sn:true;f:18");
STL(J,"c:#0000b2;o:1;s:6;sn:true;f:18");
STL(P7,"c:#966400;s:4;f:30;sp:1");
STL(Symc3,"c:#0000b2;h:1;s:6;f:30");
STL(M3,"c:#0000b2;h:1;s:6;f:30");
STL(L2,"c:#41454a;s:1;f:30;p:0");
STL(L1,"c:#51555b;s:1;f:30;p:0");
STL(Symc2,"c:#0000b2;h:1;s:6;f:18");
STL(M1,"c:#0000b2;h:1;s:6;f:18");
STL(P1,"c:#0000b2;h:1;s:6;f:18");
STL(P2,"c:#0000b2;h:1;s:6;f:18");
STL(Symc1,"c:#0000b2;h:1;s:6;f:18");
STL(Quad,"c:#798bea;s:3.5;f:30;p:500");
STL(U,"c:#cf0928;o:1;s:6;sn:true;f:18");
STL(P6,"c:#0000b2;h:2;s:6;f:30");
STL(E11,"c:#780013;h:2;s:7;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjEwO2Y6MzA=");
STL(R1,"c:#993300;h:1;s:1;f:30;p:0");
STL(Par1,"c:#780013;h:1;s:1;f:30;p:0");
STL(S1,"c:#006633;s:3;f:24");
STL(Par2,"c:#780013;h:1;s:1;f:30;p:0");
STL(Ux,"c:#0000b2;s:3.5;sn:true;f:14;sp:2");
STL(P3,"c:#b40000;h:1;o:1;s:6;sn:true;f:30");
STL(Uy,"c:#0000b2;s:3.5;sn:true;f:15;sp:2");
STL(yU,"c:#966400;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
STL(S5,"c:#006633;s:1;f:24;dh:true");
STL(xU,"c:#966400;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
STL(L11,"c:#780013;h:2;s:1;f:30;p:0");
STL(S6,"c:#3a1a39;s:1;f:24;dh:true");
STL(E2,"c:#2c69cf;s:7;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
STL(Par11,"c:#780013;h:2;s:1;f:30;p:0");
STL(Par21,"c:#780013;h:2;s:1;f:30;p:0");
STL(P4,"c:#0000b2;h:2;s:6;f:30");
STL(P5,"c:#0000b2;h:2;s:6;f:30");
STL(M2,"c:#0000b2;h:2;s:6;f:30");
STL(M11,"c:#0000b2;h:2;s:6;f:30");
STL(L21,"c:#780013;h:2;s:1;f:30;p:0");
STL(Par31,"c:#780013;h:1;s:1;f:30;p:0");
STL(Par5,"c:#2c69cf;h:1;s:2;f:30;p:0");
STL(P15,"c:#0000b2;h:1;s:6;f:30");
STL(V,"c:#cf0928;o:1;s:6;sn:true;f:18");
STL(Par3,"c:#780013;h:1;s:1;f:30;p:0");
STL(S9,"c:#cc66cc;s:1;f:24;dh:true");
STL(S2,"c:#006633;s:3;f:24");
STL(M,"c:#ea15e4;s:6;sn:true;f:17");
STL(Par4,"c:#780013;h:1;s:1;f:30;p:0");
STL(R2,"c:#3a1a39;h:1;s:1;f:30;p:0;dh:true");
STL(S4,"c:#cc66cc;s:1;f:24;dh:true");
STL(Vy,"c:#0000b2;s:3.5;sn:true;f:14;sp:2");
STL(Vx,"c:#0000b2;s:3.5;sn:true;f:14;sp:2");
STL(S3,"c:#ea15e4;s:2;f:24");
STL(xV,"c:#966400;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
STL(S8,"c:#3a1a39;s:1;f:24;dh:true");
STL(K,"c:#4633db;s:6;sn:true;f:18");
STL(S7,"c:#3a1a39;s:1;f:24;dh:true");
STL(yV,"c:#966400;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
STL(E4,"c:#cf0928;s:7;f:16;p:7;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E3,"c:#2c69cf;s:7;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E1,"c:#2c69cf;s:7;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxOA==");
SetCoordsStyle("isAxis:false;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:false;color:#111111;fontSize:18;axisWidth:1;gridWidth:0.1");
SetGeneralStyle("background-color:#ffffff");