# A cone being intercepted by a slanted plane

I have the 3d cone:

Plot3D[-Sqrt[x^2 + y^2], {x, -20, 20}, {y, -20, 20}, Mesh -> None,
BoxRatios -> {1, 1, 1}]


I need a slanted plane intersecting it. Can somebody help me?

• Add a plane to your plot? e.g. Plot3D[{-Sqrt[x^2 + y^2], -1 - x - y}, {x, -1, 1}, {y, -1, 1}] Feb 26, 2015 at 0:10
• I don't quite get what you're after. You know the equation of a cone but not of a plane? Any linear function of x and y yields a plane. Feb 26, 2015 at 0:19

Graphics3D[
{
{Opacity[0.5], Cone[{{0,0,0}, {0,0,3}}, 1]},
{Yellow, Opacity[0.5], Polygon[{{-1,-1,1}, {-1,1,1}, {1,1,2}, {1,-1,2}, {-1,-1,1}}]}
}
]


Or play around with this:

Manipulate[
Graphics3D[
{
{LightBlue, Opacity[0.5], Cone[{{0, 0, 0}, {0, 0, 3}}, rcone]},
{Yellow, Opacity[0.5],
Polygon[{{-1,-1,1}, {-1,1,1}, {1,1,m}, {1,-1,m}, {-1,-1,1}}]}
}
],
{rcone, .5, 2}, {m, 1, 3}
]


let's say you have a plane:

myPlane=-8-x-2y


you can use Plot3D like so;

Plot3D[{-Sqrt[x^2 + y^2], myPlane}, {x, -15, 15}, {y, -15, 15},
Mesh -> None, BoxRatios -> {1, 1, 1}, PlotLegends -> "Expressions"]


you can pimp your plot with RegionFunction:

Plot3D[{-Sqrt[x^2 + y^2], myPlane}, {x, -15, 15}, {y, -15, 15},
RegionFunction -> Function[{x, y, z}, -10 < z < 10], BoxRatios -> 1,
PlotLegends -> "Expressions"]


and or and specify ViewPoint for visualization: