Conic Sections

Cone z=((((x^2)+(y^2)))^(1/2))=(Sqrt[(x^2)+(y^2)])

Define Function

f[x_,y_]:=Sqrt[x^2+y^2];

3D Surface Plot - Standard Style

P1zero = Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic,ColorFunction->"TemperatureMap"]

P1 = Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])",BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic,ColorFunction->"TemperatureMap"];

P2 = Plot3D[-f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"x","y","z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])", BoxRatios->Automatic,ColorFunction->"TemperatureMap"];

Show[{P1,P2}, PlotRange->All]

Contour Plot of z = f(x,y) Level Curves

ContourPlot[f[x,y],{x,-2,2},{y,-2,2}, FrameLabel->{"X","Y"}, PlotLabel->"Level Curves For z=(Sqrt[(x^2) + (y^2)])", ColorFunction->"TemperatureMap", Contours -> 40,BaseStyle->Directive[FontSize->16, FontFamily->"Times"]]

3D Surface Plot - Hue Color Function Option

P1 = Plot3D[f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])", ColorFunction->Function[{x,y,z},Hue[z]],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic];

P2 = Plot3D[-f[x,y],{x,-2,2},{y,-2,2}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])", ColorFunction->Function[{x,y,z},Hue[z]],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic];

Show[{P1,P2}, PlotRange->All]

3D Surface Plot  RegionFunction restriction to circular domain

P1 = Plot3D[f[x,y],{x,-3,3},{y,-3,3}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])", ColorFunction->Function[{x,y,z},Hue[z]], RegionFunction->Function[{x,y,z},x^2+y^2≤ 9],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic];

P2 = Plot3D[-f[x,y],{x,-3,3},{y,-3,3}, AxesLabel->{"X","Y","Z"}, PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)])", ColorFunction->Function[{x,y,z},Hue[z]], RegionFunction->Function[{x,y,z},x^2+y^2≤ 9],BaseStyle->Directive[FontSize->16, FontFamily->"Times"], BoxRatios->Automatic];

Show[{P1,P2}, PlotRange->All]

The plane x=1.5 intersects the cone to form a hyperbola

IntersectPlanePlot1 = ParametricPlot3D[{1.5, s,t},{s,-3,3},{t,-3,3},PlotStyle->Cyan];

Show[P1,P2,IntersectPlanePlot1, PlotRange->All,PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)]) intersecting plane x = 1.5"]

The plane z=x+1 intersects the cone to form a parabola

IntersectPlanePlot2 = Plot3D[x+1,{x,-2,2},{y,-2,2},PlotStyle->Yellow];

Show[P1,P2,IntersectPlanePlot2, PlotRange->All,PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)]) intersecting plane z=x+1"]

The plane z=x/2+1 intersects the cone to form an ellipse

IntersectPlanePlot2 = Plot3D[x/2+1,{x,-2,3},{y,-2,2},PlotStyle->Yellow];

Show[P1,P2,IntersectPlanePlot2, PlotRange->All,PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)]) intersecting plane z=x/2+1"]

The plane z=1 intersects the cone to form a circle

IntersectPlanePlot2 = Plot3D[1,{x,-2,2},{y,-2,2},PlotStyle->Yellow];

Show[P1,P2,IntersectPlanePlot2, PlotRange->All,PlotLabel->"Plot of Surface z=(Sqrt[(x^2) + (y^2)]) intersecting plane z=1"]