Working Material

Oblate Spheroid with Trigonometric Parametric Equations

Alejandro Latorre Chirot

Author

Alejandro Latorre Chirot

Title

Oblate Spheroid with Trigonometric Parametric Equations

Description

This animation shows how a point moves in such a way that the sum of the squares of its distances to the X and Y axes is always equal to 4. An oblate spheroid is formed.

Oblate Spheroid with Trigonometric Parametric Equations

Alejandro Latorre Chirot

LugarGeometricoSuperficies8Parametricas::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d1=N[4

(Cos[x1]Sin[x1/2])

(Sin[x1])

];d2=N[4

(Cos[x1]Cos[x1/2])

(Sin[x1])

];w=Grid

(P-X)

(P-Y)

,SUMA,{d1,d2,d1+d2},FrameAll,ItemStyle->12;Show[ParametricPlot3D[2Cos[v]Cos[u],2Cos[v]Sin[u],

Sin[v],{u,0,π},{v,0,2π},Mesh->None,PlotStyleDirective[Green,Opacity[0.3],Specularity[White,30]],PerformanceGoal"Quality"],Graphics3D[Red,Ball[2Cos[x1]Cos[x1/2],2Cos[x1]Sin[x1/2],

Sin[x1],0.05]],Graphics3D[{Black,Ball[{2Cos[x1]Cos[x1/2],0,0},0.05]}],Graphics3D[{Black,Ball[{0,2Cos[x1]Sin[x1/2],0},0.05]}],Graphics3D[Black,Dashed,Thick,Line[2Cos[x1]Cos[x1/2],2Cos[x1]Sin[x1/2],

Sin[x1],{2Cos[x1]Cos[x1/2],0,0}]],Graphics3D[Black,Dashed,Thick,Line[2Cos[x1]Cos[x1/2],2Cos[x1]Sin[x1/2],

Sin[x1],{0,2Cos[x1]Sin[x1/2],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 (

)"},-7,7,0.1},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

Out[]=

Lugar geométrico: esferoide oblato:

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
1.14301	2.85699	4.

Cite this as: Alejandro Latorre Chirot, "Oblate Spheroid with Trigonometric Parametric Equations" from the Notebook Archive (2024), https://notebookarchive.org/2024-08-9puz8kd