GeometricLocusQuadric::usage="Obtain an equation for the surface consisting of the points P for which the distance from P to the X axis is twice the distance from P to the YZ plane. Identify the surface. References: Internet: eodelgadocursos.wordpress.com, 12.6, prob.- 46; Personal. ";
Aplicando la información:
2
y
+
2
z
=
2x
1
2
y
+
2
z
-4
2
x
=0
In[]:=
Manipulated1=
2
(2x1Cos[x1])
+
2
(2x1Sin[x1])
;d2=Abs[x1];​​w=Grid[
EjeX-P
,
P-YZ
,{d1,d2},FrameAll,ItemStyle->15];​​Show[{ParametricPlot3D[{v,2vCos[u],2vSin[u]},{u,0,2π},{v,-10,10},Mesh->None,PlotStyleDirective[Orange,Opacity[0.3],Specularity[White,30]],PerformanceGoal"Quality"],ContourPlot3D[x==0,{x,-20,20},{y,-20,20},{z,-20,20},Mesh->None,ContourStyleDirective[Blue,Opacity[0.3],Specularity[White,30]],PerformanceGoal"Quality"],Graphics3D[{Red,Ball[{x1,2x1Cos[x1],2x1Sin[x1]},0.48]}],Graphics3D[{Black,Ball[{0,2x1Cos[x1],2x1Sin[x1]},0.45]}],Graphics3D[{Black,Ball[{x1,0,0},0.45]}],Graphics3D[{Black,Dashed,Thick,Line[{{x1,2x1Cos[x1],2x1Sin[x1]},{0,2x1Cos[x1],2x1Sin[x1]}}]}],Graphics3D[{Green,Dashed,Thick,Line[{{x1,2x1Cos[x1],2x1Sin[x1]},{x1,0,0}}]}]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll],Style["Elliptic cone:",Bold,Large],{{x1,0,"Value (​
x
1
​)"},-9,9,0.1},Delimiter,w,2,"Distances",ControlPlacementTop
Out[]=
​
Elliptic cone:
Value (​
x
1
​)
Distances
EjeX-P
P-YZ
16.4
8.2