Section 12.6 — Quadric Surfaces
Prof Kevin G. TeBeest
Kettering University

This is Example 1 in the text.
Graph the parabolic cylinder z = x^2
> z := x^2;

z := x^2

> plot3d( z, x = -3.0 .. 3.0, y = -3.0 .. 3.0, axes = framed ) ;

[Maple Plot]

Unassign z:

> z := 'z' ;

z := 'z'

This is Example 2(a) in the text.
Graph the circular cylinder x^2+y^2 = 1
> with( plots, implicitplot3d );

[implicitplot3d]

> implicitplot3d( x^2 + y^2 = 1, x = -1.0 .. 1.0, y = -1.0 .. 1.0, z = -1.0 .. 1.0, axes=framed ) ;

[Maple Plot]

This is Example 3 in the text.
Graph the ellipsoid x^2+y^2/9+z^2/4 = 1
> implicitplot3d( x^2 + y^2/9 + z^2/4 = 1, x = -1.0 .. 1.0, y = -3.0 .. 3.0, z = -2.0 .. 2.0, axes = framed, style = patchcontour ) ;

[Maple Plot]

This is Example 4 in the text.
Graph the elliptic paraboloid z = 4*x^2+y^2
> z := 4 * x^2 + y^2 ;

z := 4*x^2+y^2

> plot3d( z, x = -3.0 .. 3.0, y = -5.0 .. 5.0, axes = framed ) ;

[Maple Plot]

This is Example 5 in the text.
Graph the hyperbolic paraboloid z = y^2-x^2
This is a "saddle". What potato chip does it remind you of?

> z := y^2 - x^2 ;

z := y^2-x^2

> plot3d( z, x = -4.0 .. 4.0, y = -4.0 .. 4.0, axes=framed ) ;

[Maple Plot]

This is Example 6 in the text.
Graph the hyperboloid of one sheet x^2/4+y^2-z^2/4 = 1
First unassign z:

> z := 'z' ;

z := 'z'

> implicitplot3d( x^2/4 + y^2 - z^2/4 = 1, x = -6.0 .. 6.0, y = -3.0 .. 3.0, z = -4.0 .. 4.0, axes = framed, style = patchcontour ) ;

[Maple Plot]

This is Example 7 in the text
Graph the hyperboloid of two sheets 4*x^2-y^2+2*z^2+4 = 0
> implicitplot3d( 4*x^2 - y^2 + 2*z^2 + 4 = 0, x = -8.0 .. 8.0, y = -15.0 .. 15.0, z = -12.0 .. 12.0, axes = framed, style = patchcontour, grid = [20,20,20] ) ;

[Maple Plot]

Graph the cone y^2 = x^2+2*z^2

> implicitplot3d( y^2 = x^2 + 2*z^2, x = -10.0 .. 10.0, y = -10.0 .. 10.0, z = -10.0 .. 10.0, axes = framed, style = patchcontour, grid = [30,30,30] ) ;

[Maple Plot]

Dr. K. G. TeBeest
Applied Mathematics
Kettering University