EllipsePlaneSurfaceRevolution::usage="The ellipse {3 Cos[θ], 3 Sin[θ], 6 Cos[θ]} it is located on the plane z = 2x. First it will be rotated around the straight line t{1, 0, 2} and then around the straight line t{2, 0, -1} to observe what surfaces of revolution are generated. Reference: Personal. ";
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Show[{ParametricPlot3D[{3Cos[θ],3Sin[θ],6Cos[θ]},{θ,0,2π}],ContourPlot3D[z==2x,{x,-5,5},{y,-5,5},{z,-6,6}],ParametricPlot3D[{t,0,2t},{t,-4,4}],ParametricPlot3D[t{2,0,-1},{t,-8,8}]}]
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Manipulate[Show[{RevolutionPlot3D[{3Cos[t],3Sin[t],6Cos[t]},{t,0,2π},{θ,0,θ1},RevolutionAxis{1,0,2},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",PlotPoints->60],​​ParametricPlot3D[t{1,0,2},{t,-4,4},ColorFunction->"BlueGreenYellow",PlotStyleThick]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{6,-2.4,2.},ImageSize700],Style["Surface of revolution 1:",Bold,Large],{{θ1,1,"Value (θ)"},0.00001,2π,0.00001},ControlPlacementTop]
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Surface of revolution 1:
Value (θ)
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Manipulate[Show[{RevolutionPlot3D[{3Cos[t],3Sin[t],6Cos[t]},{t,0,2π},{θ,0,θ1},RevolutionAxis{2,0,-1},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",PlotPoints->60],​​ParametricPlot3D[t{2,0,-1},{t,-4,4},ColorFunction->"BlueGreenYellow",PlotStyleThick]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{6,-2.4,2.},ImageSize700],Style["Surface of revolution 2:",Bold,Large],{{θ1,1,"Value (θ)"},0.00001,2π,0.00001},ControlPlacementTop]
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Surface of revolution 2:
Value (θ)