In[]:=
ConicalSection::usage="The right circular cone is visualized + - = 0 and the plane that intersects it a1 x + b1 y + c1 z = d1, when manipulatingthe coefficients of the plane, the different conical sections are formed in space. ";Manipulateee=2+;α=ArcSin+++;γ[u_]:={(d1/(a1Cos[u]+b1Sin[u]+c1))Cos[u],(d1/(a1Cos[u]+b1Sin[u]+c1))Sin[u],(d1/(a1Cos[u]+b1Sin[u]+c1))};If[ee<1,g$=Ellipse];If[ee==1,g$=Parabola];If[ee>1,g$=Hyperbola];q=Grid[{{Plane,Angleº,Eccentricity,Genus,ConicalSection},{{a1,b1,c1,d1},α,ee,g$,γ[u]}},FrameAll,ItemSize->20,ItemStyle->13];Show[{ContourPlot3D[a1x+b1y+c1z==d1,{x,-10,10},{y,-10,10},{z,-10,10},Mesh->None,ContourStyleDirective[Yellow,Opacity[0.8],Specularity[White,30]]],ParametricPlot3D[{vCos[u],vSin[u],v},{u,0,2π},{v,-10,10},PlotStyle->Directive[Blue,Opacity[0.3],Specularity[White,30]],MeshFalse,PerformanceGoal->"Quality"],ParametricPlot3D[γ[t],{t,0,2π},PlotStyle->Black]/.Line[pts_,rest___]:>Tube[pts,0.1,rest]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PerformanceGoal"Quality",BoxRatios->Automatic],Style["You have to vary the coefficients and the independent term of the equation of the plane x + y + z = that intersects with the cone + - = 0 to get the conical section:",Bold,Medium],{{a1,-9.9,"Coefficient "},-10,10,0.1},Delimiter,{{b1,-9.9,"Coefficient "},-10,10,0.1},Delimiter,{{c1,-9.9,"Coefficient "},-10,10,0.1},Delimiter,{{d1,-9.9,"Independent term "},-10,10,0.1},Delimiter,{{q,0,"Results:"}},ControlPlacementLeft
2
x
2
y
2
z
2
a1
2
b1
2(++)
2
a1
2
b1
2
c1
180
π
2
a1
2
b1
2
a1
2
b1
2
c1
a
1
b
1
c
1
d
1
2
x
2
y
2
z
a
1
b
1
c
1
d
1
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