GeometricLocusEquidistPoint::usage="Find the cartesian equation of the geometric locus of the points in
3

​that they are equidistant from the YZ plane and the line ℒ = {1, 0, z}. References: Internet: Repositorio.pucp.pe, 1.2 Superficies Notables en ​
3

​, Superficies cuádricas, Ejercicios propuestos, prob.- 4.; Personal. ";
Obtaining the equation of the geometric locus:
ℒ={1,0,z};
x=
2
(x-1)
+
2
y
;
In[]:=
Expand[
2
(x-1)
+
2
y
-
2
x
]
1-2x+
2
y
=0;
In[]:=
Manipulated1=
1
2
+
1
2
2
y1
;d2=
2
1
2
2
y1
-
1
2
+
2
y1
;p=Grid[
P-YZ
,
P-ℒ
,{d1,d2},FrameAll,ItemSize->15,ItemStyle->15];ShowParametricPlot3D[{1,0,z},{z,-4,4},ColorFunction->"BlueGreenYellow"],ContourPlot3D[1-2x+
2
y
==0,{x,-8.5,8.5},{y,-4,4},{z,-4,4},ContourStyle->Directive[Yellow,Opacity[0.2],Specularity[White,30]],MeshFalse,PerformanceGoal->"Quality"],ContourPlot3D[x==0,{x,-4,4},{y,-4,4},{z,-4,4},ContourStyle->Directive[Blue,Opacity[0.2],Specularity[White,30]],MeshFalse,PerformanceGoal->"Quality"],Graphics3DRed,Ball
1
2
+
1
2
2
y1
,y1,y1,0.08,Graphics3D[{Black,Ball[{0,y1,y1},0.08]}],Graphics3D[{Black,Ball[{1,0,y1},0.08]}],Graphics3DBlack,Dashed,Thick,Line
1
2
+
1
2
2
y1
,y1,y1,{0,y1,y1},Graphics3DBlack,Dashed,Thick,Line
1
2
+
1
2
2
y1
,y1,y1,{1,0,y1},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{1.3,-2.4,2.},ImageSize900,Style["Geometric locus:",Bold,Large],{{y1,1,"Value (y)"},-4,4,0.1},Delimiter,{{p,2,"Distance from the point to the YZ plane and from the point to the line ℒ"}},ControlPlacementTop
Out[]=
​
Geometric locus:
Value (y)
Distance from the point to the YZ plane and from the point to the line ℒ
P-YZ
P-ℒ
0.745
0.745