Wolfram Cloud Document

DandelineSpheresEllipseCase(improved)::usage="Spheres tangent to a pane and a cone, their points of contact with the plane determine the foci of an ellipse in space formed by the intersection of the plane and the cone. References: Wolfram MathWorld, Dandeline Spheres; Personal. ";

In[]:=

Manipulatej[x_,y_]:=

x;a1=

;b1=0;c1=-1;d1=-

;γ[t_]:={(d1/(a1Cos[t]+b1Sin[t]+c1))Cos[t],(d1/(a1Cos[t]+b1Sin[t]+c1))Sin[t],d1/(a1Cos[t]+b1Sin[t]+c1)};ζ[t_]:={10Cos[t],10Sin[t],10};

[t_]:={Cos[t],Sin[t],1};d11[t_]:=NNorm--

,0,

+γ[t];d22[t_]:=NNorm-

,0,

+γ[t];d3[t_]:=d11[t]+d22[t];d4[t_]:=N[Norm[ζ[t]-γ[t]]];d5[t_]:=N[Norm[

[t]-γ[t]]];d6[t_]:=d4[t]+d5[t];w=Grid[{{

,2a},{d11[θ1],d22[θ1],d3[θ1]}},FrameAll,ItemSize->15,ItemStyle->15];o=Grid[{{QP,PT,QP+PT},{d4[θ1],d5[θ1],d6[θ1]}},FrameAll,ItemSize->15,ItemStyle->15];ShowParametricPlot3D[{vCos[u],vSin[u],v},{u,0,2π},{v,-20,20},PlotStyleDirective[Green,Specularity[White,20],Opacity[0.1]],MeshFalse,PerformanceGoal"Quality"],ParametricPlot3D[

Cos[u]Sin[v],

Sin[u]Sin[v],

Cos[v]+2,{u,0,2π},{v,0,π},ColorFunction"LightTemperatureMap",MeshFalse,PerformanceGoal"Quality"],ParametricPlot3D[10

Cos[u]Sin[v],10

Sin[u]Sin[v],10

Cos[v]+20,{u,0,2π},{v,0,π},ColorFunction"LightTemperatureMap",MeshFalse,PerformanceGoal"Quality"],Plot3D[j[x,y],{x,-10,10},{y,-10,10},PlotStyleDirective[Yellow,Opacity[0.1]],MeshFalse,PerformanceGoal"Quality"],ParametricPlot3D[ζ[t],{t,0,2π},PlotStyle->{Green},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],ParametricPlot3D[

[t],{t,0,2π},PlotStyle{Green},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],ParametricPlot3D[γ[θ],{θ,0,θ1},PlotStyle->{Yellow},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],Graphics3DBlack,Ball-

,0,

,0.25,Graphics3DBlack,Ball

,0,

,0.25,Graphics3D[{Yellow,Ball[N[γ[θ1]],0.25]}],Graphics3D[{Green,Ball[N[ζ[θ1]],0.25]}],Graphics3D[{Green,Ball[N[

[θ1]],0.25]}],Graphics3DBlack,Dashed,Thick,LineN[γ[θ1]],-

,0,

,Graphics3DBlack,Dashed,Thick,LineN[γ[θ1]],

,0,

,Graphics3D[{Green,Thick,Line[{ζ[θ1],

[θ1]}]}]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},MeshFalse,AxesTrue,BoxedFalse,PlotRange{-20,30},ViewPoint{1.3,-2.4,-0.5},ImageSize900,Style["Dandelin Spheres Ellipse Case (improved):",Bold,Large],{{θ1,0.00002,"Angle (θ)"},0.00001,2π,0.00001},Delimiter,w,2,"Magnitudes of the vector radii of the ellipse, Sum",Delimiter,o,3,"Distance from the upper sphere to the ellipse, Distance from the lower sphere to the ellipse, Sum",ControlPlacementTop

Out[]=

Dandelin Spheres Ellipse Case (improved):

Angle (θ)

Magnitudes of the vector radii of the ellipse, Sum

PF 1	PF 2	2a
10.8917	1.83627	12.7279

Distance from the upper sphere to the ellipse, Distance from the lower sphere to the ellipse, Sum

QP	PT	PT+QP
1.83627	10.8917	12.7279