Wolfram Cloud Document

DandelineSpheresHyperbolaCase(improved)::usage="Spheres tangent to a plane and a cone, but each in different leafs of the cone, and their points of contact with the plane determine the foci of a hyperbola in space formed by the intersection of the plane and the cone. Reference: Personal. ";

In[]:=

Manipulatej[x_,y_]:=24-7x;a1=7;b1=0;c1=1;d1=24;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_]:={2Cos[t],2Sin[t],2};φ[t_]:={3Cos[t],3Sin[t],-3};d11[t_]:=NNormγ[t]-

,0,

;d22[t_]:=NNormγ[t]-

,0,-

;d3[t_]:=Abs[d11[t]-d22[t]];d4[t_]:=N[Norm[φ[t]-ζ[t-π]]];p=Grid[{{

,2a},{d11[θ1],d22[θ1],d3[θ1]}},FrameAll,ItemSize->15,ItemStyle->15];o=Grid[{{

},{d4[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[2

Cos[u]Sin[v],2

Sin[u]Sin[v],2

Cos[v]+4,{u,0,2π},{v,0,π},ColorFunction"LightTemperatureMap",MeshFalse,PerformanceGoal"Quality"],ParametricPlot3D[3

Cos[u]Sin[v],3

Sin[u]Sin[v],3

Cos[v]-6,{u,0,2π},{v,0,π},ColorFunction"LightTemperatureMap",MeshFalse,PerformanceGoal"Quality"],Plot3D[j[x,y],{x,-14,14},{y,-14,14},PlotStyle->Directive[Yellow,Specularity[White,20],Opacity[0.2]],MeshFalse,PerformanceGoal"Quality"],ParametricPlot3D[γ[t],{t,0,θ1},PlotStyle{Yellow},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],ParametricPlot3D[ζ[θ],{θ,0,2π},PlotStyle->{Green},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.08,rest],ParametricPlot3D[φ[θ],{θ,0,2π},PlotStyle->{Green},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[φ[θ1-π]],0.25]}],Graphics3D[{Green,Ball[N[ζ[θ1]],0.25]}],Graphics3DBlack,Dashed,Thick,LineN[γ[θ1]],

,0,

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

,0,-

,Graphics3D[{Green,Line[{φ[θ1-π],ζ[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14,ViewPoint{6,4,-1.3},ImageSize900,Style["Dandeline Spheres Hyperbola Case (improved):",Bold,Large],{{θ1,0.00002,"Angle (θ)"},0.00001,2π,0.00001},Delimiter,p,1,"Magnitudes of the vectors radii of the hyperbola, Substraction",Delimiter,o,3,"Distance between spheres through to the origin",ControlPlacementTop

Out[]=

Dandeline Spheres Hyperbola Case (improved):

Angle (θ)

Magnitudes of the vectors radii of the hyperbola, Substraction

PF 1	PF 2	2a
1.41421	8.48528	7.07107

Distance between spheres through to the origin

7.07107