Quadric Surfaces

12.6 1-6

Let's use Mathematica to plot all the surfaces, and then match them.

1

surface= x^2+y^2+4z^2-10
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

1) ellipsoid, matches d.

2

surface= z^2+4y^2-4x^2-4
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

2) Matches i, hyperboloid of one sheets

3

surface=9y^2+z^2-16
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

3) Cylinder, matches a.

4

surface=y^2+z^2-x^2
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

4) matches g, elliptical cone

5

surface=x-y^2+z^2
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

5) matches k, saddle point

6

surface=x+y^2+z^2
surfaceplot = ContourPlot3D[surface,{x,-5,5},{y,-4,4},{z,-7,7},Axes->True,Contours->0,AxesLabel->{"x-axis","y-axis","z-axis"}]

6) matches e, elliptical paraboloid

12.80 a

Integrate[π a b(1+((z^2)/(c^2))),{z,0,h}]