Working Material

Oblate Ellipsoid

Alejandro Latorre Chirot

Author

Alejandro Latorre Chirot

Title

Oblate Ellipsoid

Description

This animation shows how a point moves on surface such the sum of the squares of their distances to the X and Y axis are 4.

Oblate Ellipsoid

Alejandro Latorre Chirot

LugarGeometricoSuperficies8::usage="Hallar e identificar la ecuación del lugar geométrico de un punto que se mueve de tal manera que la suma de los cuadrados de sus distancias a los ejes X e Y es siempre igual a 4. Construir la superficie. Respuesta:

+ 2

= 4. Referencia: Geometría Analítica, Charles H. Lehmann, Ed. Limusa (2003). Prob.- 8, pág.- 437.";

Aplicando la información:

In[]:=

Expand

Norm[{1,0,0}{-x,-y,-z}]

Norm[{1,0,0}]

Norm[{0,1,0}{-x,-y,-z}]

Norm[{0,1,0}]

-4

-4+

Abs[x]

Abs[y]

Abs[z]

;

=4;

In[]:=

Manipulateli=-

;ls=

;z1=

;z11=-

;d1=N[

];d2=N[

];w=Grid

(P-X)

(P-Y)

,SUMA,{d1,d2,d1+d2},FrameAll,ItemStyle->12;Show[ContourPlot3D[

==4,{x,-2,2},{y,-2,2},z,-

,Mesh->None,ContourStyleDirective[Green,Opacity[0.3],Specularity[White,30]],PerformanceGoal"Quality"],Graphics3D[{Red,Ball[{x1,y1,z1},0.05]}],Graphics3D[{Red,Ball[{x1,y1,z11},0.05]}],Graphics3D[{Black,Ball[{x1,0,0},0.05]}],Graphics3D[{Black,Ball[{0,y1,0},0.05]}],Graphics3D[{Black,Dashed,Thick,Line[{{x1,y1,z1},{x1,0,0}}]}],Graphics3D[{Black,Dashed,Thick,Line[{{x1,y1,z11},{x1,0,0}}]}],Graphics3D[{Black,Dashed,Thick,Line[{{x1,y1,z1},{0,y1,0}}]}],Graphics3D[{Black,Dashed,Thick,Line[{{x1,y1,z11},{0,y1,0}}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ImageSizeFull,ViewPoint{1.3,-2.4,2.}],Style["Lugar geométrico: esferoide oblato:",Bold,Medium],{{x1,1,"Valor (

)"},-2,2,0.1},Delimiter,{{y1,1,"Valor (

)"},li,ls,0.1},Delimiter,{{w,2,"Distancia al cuadrado del punto P al eje X, Distancia al cuadrado del punto P al eje Y y la suma"}},ControlPlacementLeft,AutoAction->True

Out[]=

Lugar geométrico: esferoide oblato:

Valor (

)

Valor (

)

Distancia al cuadrado del punto P al eje X, Distancia al cuadrado del punto P al eje Y y la suma

2 (P-X)	2 (P-Y)	SUMA
2.7	1.3	4.

Cite this as: Alejandro Latorre Chirot, "Oblate Ellipsoid" from the Notebook Archive (2024), https://notebookarchive.org/2024-08-478q8mu