EllipseRotatedX::usage="Find the cartesian equation of the surface of revolution S generated by the rotation of the ellipseξ:
2
x
+
2
y
4
= 1, z = 0.around the X axis.References: Internet: Repositorio.pucp.pe, 1.2 Superficies Notables en
3

​, Superficie de revolución,​Ejercicios propuestos, prob.- 2; Personal ";
Development
ξ=x,±2
1-
2
x
,0;​​Q={x,0,0};
P={x,y,z};​​
P
0
=
x
0
,±2
1-
2
x
0
,0;​​d(P,Q)=d(
P
0
,Q);​​4
2
x
+
2
y
+
2
z
=4;
In[]:=
gr=ShowParametricPlot3Dx,2
1-
2
x
,0,{x,-1,1},ColorFunction->"DeepSeaColors",ParametricPlot3D[t{1,0,0},{t,-2,2},ColorFunction->"BlueGreenYellow"],ContourPlot3D[4
2
x
+
2
y
+
2
z
==4,{x,-1,1},{y,-2,2},{z,-2,2},ContourStyle->Directive[Yellow,Opacity[0.2],Specularity[White,30]],MeshFalse,PerformanceGoal->"Quality"],Graphics3D[{Black,Ball[{0,0,0},0.05]}],Graphics3D[{Black,Ball[{0,2,0},0.05]}],Graphics3D[{Black,Dashed,Thick,Line[{{0,0,0},{0,2,0}}]}],​​AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll
Out[]=
In[]:=
ResourceFunction["SpinShow"][gr,30]
Out[]=