GraphingCalculator 3.2;
Window 44 6 754 776;
PaneDivider 101;
BackgroundColor 0 0 0;
BackgroundType 0;
Slider -1.95 1.95;
SliderSteps 78;
SliderControlValue 11;
SliderThrottle 20;
T 0 6.28318530717959;
U -2 2;
V 0 6.28318530717959;
2Dp.BottomLeft -3.78125 -2.984375;
3D.X -2.2 2.2;
3D.Y -2.2 2.2;
3D.Z -2.2 2.2;
3D.View 0.567540183617332 -0.785650132947371 -0.246276285053136 0.725246376662837 0.618630191777373 -0.302182691362494 0.389763817095951 -0.00711016325092326 0.92088740487726;
3D.Rotation 1 0 0 0 1 0 0 0 1;
Text "<size=13>The left pane shows the horizontal plane <I>z </I>= <I>n</I> intersecting the hyperboloid of one 
sheet <I>x</I>^2 + <I>y</I>^2 – <I>z</I>^2 = 1. The trace formed by the intersection is graphed on the
 <I>xy</I>-plane shown in the right pane.  
Move the slider (or press the play button) below to change the position of the plane.



";
Color 6;
Grain 0.55;
Expr z=n;
Color 17;
Grain 0.883333333333333;
Expr x^2+y^2-z^2=1;
Color 7;
Opacity 0.7;
Expr vector(x,y,z)=vector(sqrt(1+u^2)*cos(v),sqrt(1+u^2)*sin(v),u);
Color 2;
Grain 0.833333333333333;
Expr vector(x,y,z)=vector([sqrt(n^2+1)+0.01]*cos(t),[sqrt(n^2+1)+0.01]*sin(t),n);
Color 2;
Expr vector(prime(x),prime(y))=vector([sqrt(n^2+1)]*cos(t),[sqrt(n^2+1)]*sin(t));