// Macros :
$macros={};
$macros["Parabole3pts"]={
	name:"Parabole3pts",
	parameters:["point","point","point"],
	exec:
	function (A,B,C){
Den=Expression("Den","Den=","","","x(A)(x(C)^2-x(B)^2)+x(B)x(C)*(x(B)-x(C))+x(A)^2*(x(B)-x(C))","-12.291987897706957","4.986348565400363");
NumB=Expression("NumB","NumB = ","","","x(A)^2*(y(C)-y(B))-x(B)^2*y(C)+y(B)*x(C)^2+y(A)*(x(B)^2-x(C)^2)","-0.1875217050304001","4.986348565400363");
NumC=Expression("NumC","NumC = ","","","x(A)*(y(B)x(C)^2-x(B)^2*y(C))+x(A)^2*(x(B)y(C)-y(B)x(C))+y(A)(x(B)^2*x(C)-x(B)x(C)^2)","-16.225939410326838","7.104630149118761");
NumA=Expression("NumA","NumA = ","","","x(A)*(y(C)-y(B))-x(B)*y(C)+y(B)*x(C)+y(A)*(x(B)-x(C))","-5.937143146551764","6.499406839484933");
c=Expression("c","","","","NumC/Den","-0.792745014664228","5.894183529851105");
b=Expression("b","","","","-NumB/Den","-1.0953566694811419","7.104630149118761");
a=Expression("a","","","","NumA/Den","-0.792745014664228","8.315076768386417");
f=Expression("f","f(x) =","","","a*x^2+b*x+c","-9.265871349537818","8.617688423203331");
f1=Curvus("f1","","","a*x^2+b*x+c");
STL(c,"c:#0000b2;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(b,"c:#0000b2;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(a,"c:#0000b2;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(f,"c:#780013;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(f1,"c:#109b10;s:2.5;f:30;p:0");
return [c,b,a,f,f1];
}};

// Coordinates System :
SetCoords(518.134869247566,325.44988826147164,28.812488031331682,true);


// Geometry :
C=Point("C",11.726343465549657,5.42993330153726);
Q=Point("Q",-2.260647160243022,-6.648162821976021);
P=Point("P",-13.748721346688125,1.2997797420600177);
E4=Expression("E4","Etant donn\u00e9s deux autres points P et Q on cherche les paraboles (fonctions du 2nd deg f3 et f4)","","","1","-17.635924696784354","9.21301513332734");
E3=Expression("E3","On se donne trois points A, B, C et la fonction du second degr\u00e9 f1 passant par ces trois points (parabole bleue)","","","0","-17.635924696784354","10.25423031638883");
A=Point("A",-2.3647686785491713,-1.7891586343557353);
E5=Expression("E5","On trouve alors deux points M et N solutions pour le point de contact, et donc deux paraboles tangentes \u00e0 la premi\u00e8re","","","4","-17.635924696784354","7.13058476720436");
E6=Expression("E6","En ligne : goo.gl/XVEB3o ","","","1","-16.594709513722865","-8.140571251030822");
E7=Expression("E7","passant par P et Q et tangentes \u00e0 la premi\u00e8re parabole ","","","2","-17.635924696784354","8.17179995026585");
B=Point("B",-6.043728992033102,5.742297856455707);
Den=Expression("Den","Den=","","","x(A)(x(C)^2-x(B)^2)+x(B)x(C)*(x(B)-x(C))+x(A)^2*(x(B)-x(C))","-9.6532749599796","5.395226128768544");
NumB=Expression("NumB","NumB = ","","","x(A)^2*(y(C)-y(B))-x(B)^2*y(C)+y(B)*x(C)^2+y(A)*(x(B)^2-x(C)^2)","4.229594147506931","5.395226128768544");
NumA=Expression("NumA","NumA = ","","","x(A)*(y(C)-y(B))-x(B)*y(C)+y(B)*x(C)+y(A)*(x(B)-x(C))","-2.3647686785491713","7.13058476720436");
NumC=Expression("NumC","NumC = ","","","x(A)*(y(B)x(C)^2-x(B)^2*y(C))+x(A)^2*(x(B)y(C)-y(B)x(C))+y(A)(x(B)^2*x(C)-x(B)x(C)^2)","-14.165207419912722","7.8247282225786865");
b1=Expression("b1","","","","-NumB/Den","0.7588768706352982","3.659867490332728");
c1=Expression("c1","","","","NumC/Den","0.7588768706352982","2.618652307271238");
a1=Expression("a1","","","","NumA/Den","0.7588768706352982","4.701082673394217");
h1=Curvus("h1","","","a1*x^2+b1*x+c1");
suv=Expression("suv","","","","sqrt((y(P)-a1*x(P)^2-b1*x(P)-c1)*(y(Q)-a1*x(Q)^2-b1*x(Q)-c1))","-16.941781241410027","-2.934495335723374");
a3=Expression("a3","","","","(2*sqrt((y(P)-a1*x(P)^2-b1*x(P)-c1)*y(Q)+(-a1*y(P)+a1^2*x(P)^2+a1*b1*x(P)+a1*c1)*x(Q)^2+(-b1*y(P)+a1*b1*x(P)^2+b1^2*x(P)+b1*c1)*x(Q)-c1*y(P)+a1*c1*x(P)^2+b1*c1*x(P)+c1^2)+y(Q)+(-2*a1*x(P)-b1)*x(Q)+y(P)-b1*x(P)-2*c1)/(x(Q)^2-2*x(P)*x(Q)+x(P)^2)","-15.206422602974211","4.701082673394217");
f1=Expression("f1","f(x) =","","","a1*x^2+b1*x+c1","-1.6706252231748446","5.742297856455707");
a4=Expression("a4","","","","-(2*sqrt((y(P)-a1*x(P)^2-b1*x(P)-c1)*y(Q)+(-a1*y(P)+a1^2*x(P)^2+a1*b1*x(P)+a1*c1)*x(Q)^2+(-b1*y(P)+a1*b1*x(P)^2+b1^2*x(P)+b1*c1)*x(Q)-c1*y(P)+a1*c1*x(P)^2+b1*c1*x(P)+c1^2)-y(Q)+(2*a1*x(P)+b1)*x(Q)-y(P)+b1*x(P)+2*c1)/(x(Q)^2-2*x(P)*x(Q)+x(P)^2)","0.7588768706352982","-0.8520649696003945");
c4=Expression("c4","","","","(-x(P)^2*y(Q)^2+((-y(P)+3*a1*x(P)^2+b1*x(P))*x(Q)^2+(-4*x(P)*y(P)+4*a1*x(P)^3+6*b1*x(P)^2+(2*suv+6*c1)*x(P))*x(Q)-x(P)^2*y(P)+a1*x(P)^4+b1*x(P)^3+(2*suv+2*c1)*x(P)^2)*y(Q)+(a1*y(P)-2*a1^2*x(P)^2-a1*b1*x(P))*x(Q)^4+((4*a1*x(P)+b1)*y(P)-4*a1^2*x(P)^3-7*a1*b1*x(P)^2+(-2*a1*suv-6*a1*c1-b1^2)*x(P))*x(Q)^3+(-y(P)^2+(3*a1*x(P)^2+6*b1*x(P)+2*suv+2*c1)*y(P)-2*a1^2*x(P)^4-7*a1*b1*x(P)^3+(-4*a1*suv-4*a1*c1-6*b1^2)*x(P)^2+(-4*b1*suv-8*b1*c1)*x(P))*x(Q)^2+((b1*x(P)^2+(2*suv+6*c1)*x(P))*y(P)-a1*b1*x(P)^4+(-2*a1*suv-6*a1*c1-b1^2)*x(P)^3+(-4*b1*suv-8*b1*c1)*x(P)^2+(-8*c1*suv-8*c1^2)*x(P))*x(Q))/((-x(Q)^2+2*x(P)*x(Q)-x(P)^2)*y(Q)+a1*x(Q)^4+(b1-2*a1*x(P))*x(Q)^3+(-y(P)+2*a1*x(P)^2-b1*x(P)+2*suv+2*c1)*x(Q)^2+(2*x(P)*y(P)-2*a1*x(P)^3-b1*x(P)^2+(-4*suv-4*c1)*x(P))*x(Q)-x(P)^2*y(P)+a1*x(P)^4+b1*x(P)^3+(2*suv+2*c1)*x(P)^2)","0.7588768706352982","-2.934495335723374");
c3=Expression("c3","","","","(x(P)^2*y(Q)^2+((y(P)-3*a1*x(P)^2-b1*x(P))*x(Q)^2+(4*x(P)*y(P)-4*a1*x(P)^3-6*b1*x(P)^2+(2*suv-6*c1)*x(P))*x(Q)+x(P)^2*y(P)-a1*x(P)^4-b1*x(P)^3+(2*suv-2*c1)*x(P)^2)*y(Q)+(-a1*y(P)+2*a1^2*x(P)^2+a1*b1*x(P))*x(Q)^4+((-4*a1*x(P)-b1)*y(P)+4*a1^2*x(P)^3+7*a1*b1*x(P)^2+(-2*a1*suv+6*a1*c1+b1^2)*x(P))*x(Q)^3+(y(P)^2+(-3*a1*x(P)^2-6*b1*x(P)+2*suv-2*c1)*y(P)+2*a1^2*x(P)^4+7*a1*b1*x(P)^3+(-4*a1*suv+4*a1*c1+6*b1^2)*x(P)^2+(8*b1*c1-4*b1*suv)*x(P))*x(Q)^2+(((2*suv-6*c1)*x(P)-b1*x(P)^2)*y(P)+a1*b1*x(P)^4+(-2*a1*suv+6*a1*c1+b1^2)*x(P)^3+(8*b1*c1-4*b1*suv)*x(P)^2+(8*c1^2-8*c1*suv)*x(P))*x(Q))/((x(Q)^2-2*x(P)*x(Q)+x(P)^2)*y(Q)-a1*x(Q)^4+(2*a1*x(P)-b1)*x(Q)^3+(y(P)-2*a1*x(P)^2+b1*x(P)+2*suv-2*c1)*x(Q)^2+(-2*x(P)*y(P)+2*a1*x(P)^3+b1*x(P)^2+(4*c1-4*suv)*x(P))*x(Q)+x(P)^2*y(P)-a1*x(P)^4-b1*x(P)^3+(2*suv-2*c1)*x(P)^2)","-15.206422602974211","2.618652307271238");
g1=Expression("g1","","","","f1.dx(x)","-12.082777053789743","8.17179995026585");
b4=Expression("b4","","","","(2*(x(Q)+x(P))*suv-2*x(P)*y(Q)+(2*a1*x(P)+b1)*x(Q)^2+(-2*y(P)+2*a1*x(P)^2+2*b1*x(P)+2*c1)*x(Q)+b1*x(P)^2+2*c1*x(P))/(x(Q)^2-2*x(P)*x(Q)+x(P)^2)","0.7588768706352982","-1.893280152661884");
b3=Expression("b3","","","","-(2*(x(Q)+x(P))*suv+2*x(P)*y(Q)+(-2*a1*x(P)-b1)*x(Q)^2+(2*y(P)-2*a1*x(P)^2-2*b1*x(P)-2*c1)*x(Q)-b1*x(P)^2-2*c1*x(P))/(x(Q)^2-2*x(P)*x(Q)+x(P)^2)","-15.206422602974211","3.659867490332728");
E1=Expression("E1","xM = (b1-b3)/(2*(a3-a1)) =","","","(b1-b3)/(2*(a3-a1))","-16.941781241410027","-4.322782246472027");
f3=Expression("f3","","","","a3*x^2+b3*x+c3","-16.594709513722865","5.742297856455707");
xN=Expression("xN","xN=(b1-b4)/2*(a4-a1)) = ","","","(b1-b4)/(2*(a4-a1))","-16.941781241410027","-5.71106915722068");
f4=Expression("f4","","","","a4*x^2+b4*x+c4","-1.6706252231748446","0.8832936688354218");
M=Point("M","[(b1-b3)/(2*(a3-a1)),f1((b1-b3)/(2*(a3-a1)))]","0");
k4=Curvus("k4","","","f4(x)");
N=Point("N","[xN,f1(xN)]","0");
Tgte=Expression("Tgte","","","","g1(x(M))*(x-x(M))+f1(x(M))","-12.082777053789743","6.436441311830034");
k3=Curvus("k3","","","f3(x)");
E2=Expression("E2","","","","g1(xN)*(x-xN)+f1(xN)","2.841307236758278","-8.487642978717986");
Tgt1=Curvus("Tgt1","","","Tgte(x)");
Tgt2=Curvus("Tgt2","","","E2(x)");


// Styles :
STL(C,"c:#0000b2;o:1;s:6;sn:true;f:16");
STL(Q,"c:#007c00;o:1;s:6;sn:true;f:16;np:3.6334018295784913");
STL(P,"c:#007c00;o:1;s:6;sn:true;f:16;np:3.334804137437599");
STL(E4,"c:#356320;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E3,"c:#0f1f14;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(A,"c:#0000b2;o:1;s:6;sn:true;f:16;np:0.982793723247329");
STL(E5,"c:#966400;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E6,"c:#592a7a;s:7;f:20;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E7,"c:#3c7534;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(B,"c:#0000b2;o:1;s:6;sn:true;f:16");
STL(Den,"c:#457e55;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO2g6MTtzOjEwO2Y6MTY=");
STL(NumB,"c:#457e55;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO2g6MTtzOjEwO2Y6MTY=");
STL(NumA,"c:#457e55;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO2g6MTtzOjEwO2Y6MTY=");
STL(NumC,"c:#457e55;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO2g6MTtzOjEwO2Y6MTY=");
STL(b1,"c:#0000b2;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(c1,"c:#0000b2;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(a1,"c:#0000b2;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(h1,"c:#0000b2;s:2.5;sn:true;f:30;p:0");
STL(suv,"c:#966400;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(a3,"c:#007c7c;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(f1,"c:#0000b2;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojYjQwMDAwO3M6MTA7ZjoxNg==");
STL(a4,"c:#007c00;s:7;sn:true;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(c4,"c:#007c00;s:7;sn:true;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(c3,"c:#007c7c;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(g1,"c:#b40000;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(b4,"c:#007c00;s:7;sn:true;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(b3,"c:#007c7c;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E1,"c:#1e5058;s:7;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(f3,"c:#007c7c;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(xN,"c:#966400;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(f4,"c:#007c00;s:7;sn:true;f:15;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(M,"c:#966400;s:6;sn:true;f:18;sp:2;np:2.505753488765631");
STL(k4,"c:#007c00;s:3;sn:true;f:30;p:0");
STL(N,"c:#966400;s:6;sn:true;f:25;sp:2");
STL(Tgte,"c:#b40000;h:1;s:7;sn:true;f:16;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(k3,"c:#0dc6c6;s:3;f:30;p:0");
STL(E2,"c:#070c61;h:1;s:7;f:24;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(Tgt1,"c:#b40000;s:3;sn:true;f:30;p:0");
STL(Tgt2,"c:#b40000;s:3;sn:true;f:30;p:0");
SetCoordsStyle("3Dmode:true;isAxis:true;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:false;color:#b9c0c9;fontSize:18;axisWidth:1;gridWidth:0.1");