April 1, 2010

Some conic sections

?ContourPlot

ContourPlot[x^2+y^2==5^2,{x,-5,5},{y,-5,5},Axes->True,Frame->False, AxesLabel->Automatic]

ContourPlot[x^2/5^2+y^2/2^2==1,{x,-5,5},{y,-5,5},Axes->True,Frame->False,AxesLabel->Automatic]

ContourPlot[x^2/2^2-y^2/2^2==1,{x,-5,5},{y,-5,5},Axes->True,Frame->False,AxesLabel->Automatic]

ContourPlot[x^2+x*y+y^2==15,{x,-5,5},{y,-5,5},Axes->True,Frame->False,AxesLabel->Automatic]

ContourPlot[x^2+x*y-y^2==1,{x,-5,5},{y,-5,5},Axes->True,Frame->False,AxesLabel->Automatic]

Some quadric surfaces

?ContourPlot3D

ContourPlot3D[x^2+y^2+z^2 == 5^2, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[z+5 - x^2-y^2==0, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[x^2/5^2+y^2/3^2+z^2/3^2 == 1, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[x^2/5^2+y^2/3^2+z^2/3^2 == 1, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic,ViewPoint->{7.3`,-5.4`,4.`}]

ContourPlot3D[-x^2+y^2+z^2 == 3^2, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[-x^2+y^2+z^2 == 3^2, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic,ViewPoint->{7.3`,-2.4`,6.`}]

??ContourPlot3D

ContourPlot3D[-x^2-y^2+z^2 == 1, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[-x^2-y^2+z^2 == 1, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic,ViewPoint->{7.3`,-2.4`,2.`}]

ContourPlot3D[z-x^2+y^2== 0, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[z-x^2+y^2== 0, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic,ViewPoint->{0,30,15}]

ContourPlot3D[-x^2-y^2+z^2== 0, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[-x^2-y^2+z^2 == 0, {x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic,ViewPoint->{7.3`,-2.4`,2.`}]

Problem (last 15 minutes of class).

Obtain a representation from some interesting viewpoint of the surface  (x^2) +((y )^2)+ (z^2)+ 3xy + 2xz +2yz = 7  for -15 ≤ x ≤15, -15 ≤ y ≤ 15, and -15 ≤ z ≤ 15.