GraphingCalculator 4;
Window 58 18 818 1159;
PaneDivider 372;
SignificantDigits 14;
FontSizes 14;
StackPanes 1;
2D.GraphPaper 0;
Text "Ellipse

Version 1.0 12-11-16

The handles give the center C, and the semi-major and semi-minor axes (Q1 and Q2) of the ellipse relative to the  center.";
Color 2;
Expr C=3.59375+2.640625*i;
Color 7;
Expr Q_1=7.828125+1.921875*i;
Color 7;
Expr Q_2=6.8125+4.984375*i;
Color 3;
Expr X=Re([C]),Y=Im([C]);
Color 5;
Expr X_1=Re([Q_1]),Y_1=Im([Q_1]);
Expr X_2=Re([Q_2]),Y_2=Im([Q_2]);
Color 4;
Expr R=abs(C-Q_1);
Text "Semi-major and minor- axes";
Expr a=abs(X-X_1);
Color 6;
Expr b=abs(Y-Y_2);
Color 8;
Expr a;
Expr b;
Text "Distance center-to-focus:";
Color 8;
Expr f=sqrt(abs(a^2-b^2));
Color 2;
Expr f;
Text "Eccentricity:";
Color 4;
Expr E=f/a;
Color 6;
Expr E;
Color 3;
Expr [(x-X)/a]^2+[(y-Y)/b]^2=1;
Text "Semi-major and minor axes.";
Color 7;
Expr vector(X+t*a,Y);
Color 7;
Expr vector(X,Y+t*b);
Text "Focii";
Color 5;
Expr F_1=vector(X-f,Y),F_2=vector(X+f,Y);
Color 5;
Expr F_1;
Color 4;
Expr F_2;
Text "Point on the ellipse:";
Color 3;
MathPaneSlider 19;
Expr p=slider([-1,1]);
Color 8;
Expr h=X+a-(2*a*abs(p));
Expr P=vector(h,-(sgn([p])*b*sqrt(1-[(h-X)/a]^2))+Y);
Color 17;
Expr P;
Text "Length of string used to draw ellipse remains constant:";
Color 17;
Expr t*F_1+[1-t]*P;
Color 17;
Expr t*F_2+[1-t]*P;
Color 4;
Expr abs(P-F_1)+abs(P-F_2);
Text "Put P at either end of ellipse to see why the length of the string is (a+f)+(a-f)=2a.  Put P exactly between the foci to see why it is also equal to sqrt(f^2+b^2) ... so a=sqrt(f^2+b^2).";
Color 6;
Expr 2*a;
Color 2;
Expr 2*sqrt(f^2+b^2);
Text "Ellipse in parameterized form:";
Color 17;
Expr vector(a*cos([2*pi*t]),b*sin([2*pi*t]));
Color 17;
Expr vector(X,Y)+vector(a*cos([2*pi*t]),b*sin([2*pi*t]));
Text "


Author: David A. Craig <<http://web.lemoyne.edu/~craigda>";