Rotating a non-vertical line such as the line y = -x about a vertical line such as the y axis at their point of intersection, a double napped right circular hollow cone is obtained. One of seven curves namely circle, ellipse, parabola, hyperbola, point, line and intersecting lines will be formed when a plane intersects the double napped right circular cone depending on the value of d ranging from d=-15 through to d=5 only existing to translate the plane so it may pass or not pass through the vertex and the value of a ranging from a=0 through to a=145 only existing to rotate the plane after it has been translated
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How can I descritize or say mesh the conic section which results as the intersection?
Manipulate[Show[RevolutionPlot3D[-x,{x,-10,10},MeshAutomatic,MeshStyleRGBColor[0.06`,0.16`,1.`],RevolutionAxis"Z",BoxedFalse,AxesFalse],Graphics3D[{{Opacity[1],White,{Rotate[Translate[Polygon[{{10,10,5},{-10,10,5},{-10,-10,5},{10,-10,5}}],{0,0,d}],aDegree,{0,1,0}]}}},BoxedFalse],ImageSize270],{{d,0,"Translation"},-15,5,Appearance"Labeled"},{{a,0,"Rotation"},0,145,Appearance"Labeled"}]
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Translation
-4.56728
Rotation
15.3498
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RevolutionPlot3D[-x,{x,-10,10},RevolutionAxis"Z",BoxedFalse,AxesFalse,MeshNone]
RevolutionPlot3D[-x,{x,-10,10},MeshAutomatic,MeshStyleRGBColor[0.06,0.16,1.],RevolutionAxis"Z",BoxedFalse,AxesFalse]