GraphingCalculator 3.2;
Window 44 6 750 775;
PaneDivider 178;
BackgroundColor 0 0 0;
BackgroundType 0;
FontSizes 12 11 10;
T -1 1;
3D.X -4 4;
3D.Y -4 4;
3D.Z -4 4;
3D.View 0.6657366875814 -0.680788199423403 -0.305486645099436 0.61792365154215 0.732478875592924 -0.285735992963988 0.418288206471482 0.00145751024141666 0.908313190475053;
3D.Rotation 1 0 0 0 1 0 0 0 1;
Text "<size=11>The planes x = a (in yellow), y = b (in blue), and z = c (in gray) are shown. The trace of a surface appears in red in each plane. Move the sliders to position each plane to the corresponding value. You can use the mouse to rotate the graph in any direction. What do the traces reveal about the shape of the surface?";
Color 3;
Expr a=slider([-4,4]);
Color 3;
Expr b=slider([-4,4]);
Color 3;
Expr c=slider([-4,4]);
Text "



";
Color 6;
Opacity 0.7;
Expr x=a;
Color 5;
Opacity 0.7;
Expr y=b;
Color 7;
Opacity 0.7;
Expr z=c;
Color 8;
Expr m=0.06;
Color 5;
Expr f=0.02;
Color 4;
Expr vector(x,y,z)=vector(a+f,m*cos(pi*t),m*sin(pi*t));
Color 4;
Expr vector(x,y,z)=vector(m*cos(pi*t),b+f,m*sin(pi*t));
Color 4;
Expr vector(x,y,z)=vector(m*cos(pi*t),m*sin(pi*t),c+f);
Color 2;
Grain 0.65;
Expr vector(x,y,z)=vector(a+f,4*t,4*t*sin([acos([2*a/(4*t)])]));
Color 2;
Grain 0.616666666666667;
Expr vector(x,y,z)=vector(a+f,-(4*t),4*t*sin([acos([2*a/(4*t)])]));
Color 2;
Expr vector(x,y,z)=vector(b/2*cos(pi*t),b+f,b*sin(pi*t));
Color 2;
Grain 0.683333333333333;
Expr vector(x,y,z)=vector(2*t*cos([asin([-c/(4*t)])]),4*t,c+f);
Color 2;
Grain 0.683333333333333;
Expr vector(x,y,z)=vector(2*t*cos([asin([-c/(4*t)])]),-(4*t),c+f);