Wolfram Cloud Document

DandelineSpheresParabolaCase(improved)::usage="Sphere tangent to a plane parallel to the generatrix and a cone, its point of contact with the plane determines the focus of a parabola in space formed by the intersection of the plane and the cone. The distances

and

(pointo to directrix) must the same. Reference: Personal. ";

In[]:=

Manipulatek[x_,y_]:=1;j[x_,y_]:=x+4;a1=1;b1=0;c1=-1;d1=-4;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_]:={Cos[t],Sin[t],1};l2[t_]:={-3,t,1};l21[t_]:={-3,(d1/(a1Cos[t]+b1Sin[t]+c1))Sin[t],1};QP={-3,0,1}-γ[θ1];PC=Cross[QP,{0,1,0}];N1=Norm[PC];N2=Norm[{0,1,0}];d4[t_]:=N[Norm[{-1,0,3}-γ[θ1]]];d5[t_]:=N

;p=Grid[

,{d4[θ1],d5[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"],Plot3D[j[x,y],{x,-4,4},{y,-6,6},PlotStyleDirective[Yellow,Specularity[White,20],Opacity[0.2]],MeshFalse,PerformanceGoal"Quality"],Plot3D[k[x,y],{x,-4,4},{y,-6,6},PlotStyleDirective[Gray,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,0.02,rest],ParametricPlot3D[ζ[t],{t,0,2π},PlotStyle{Green},PerformanceGoal"Quality"]/.Line[pts_,rest___]:>Tube[pts,0.02,rest],Graphics3D[Tube[{l2[-10],l2[10]},0.05]],Graphics3D[{Black,Ball[{-1,0,3},0.07]}],Graphics3D[{Yellow,Ball[N[γ[θ1]],0.07]}],Graphics3D[{Black,Ball[N[l21[θ1]],0.07]}],Graphics3D[{Black,Dashed,Thick,Line[{N[γ[θ1]],{-1,0,3}}]}],Graphics3D[{Black,Dashed,Thick,Line[{N[γ[θ1]],l21[θ1]}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},MeshFalse,AxesTrue,BoxedFalse,PlotRange4,ViewPoint{-3,2,1},ImageSize900],Style["Dandelin Spheres Parabola Case (improved):",Bold,Large],{θ1,-4.7,"Angle (θ)"},-

π,

π,0.00001,Delimiter,{{p,2,"Distance from point to focus and from point to directrix"}},ControlPlacementTop

Out[]=

Dandelin Spheres Parabola Case (improved):

Angle (θ)

Distance from point to focus and from point to directrix

PF	Pl
4.17342	4.17342