>	restart: Math 230

                                    Qu a dric Surfaces in Standard Orientations.

>	with(plots):

Warning, the name changecoords has been redefined

>	setoptions3d(style=patchcontour,scaling=unconstrained):

Ellipsoid

Elemenary example: The sphere   x^2+y^2+z^2=1

More General Formula: x^2/a^2+y^2/b^2+z^2/c^2=1

>	implicitplot3d(x^2+y^2+z^2=1,x=-1..1,y=-1..1,z=-1..1,grid=[18,18,18],orientation=[50,80]);

Elliptic Paraboloid

Elemenary example: z=x^2+y^2

More General Formula: z/c=x^2/a^2+y^2/b^2

>	implicitplot3d(z=x^2+y^2,x=-1.5..1.5,y=-1.5..1.5,z=0..2,grid=[18,18,18],orientation=[50,80]);

Hyperbolic Paraboloid

Elemenary example: z=x^2-y^2

More General Formula: z/c=x^2/a^2-y^2/b^2

>	implicitplot3d(z=x^2-y^2,x=-1..1,y=-1..1,z=-1..1,grid=[19,19,19],orientation=[50,80]);

>

Elliptic Cone

Elemenary example: z^2=x^2+y^2

More General Formula: z^2=x^2/a^2+y^2/b^2

>	implicitplot3d(z^2=x^2+y^2,x=-1..1,y=-1..1,z=-1..1,grid=[19,19,19],orientation=[50,80]);

>

Hyperboloid of One Sheet

Elemenary example: z^2+1=x^2+y^2

More General Formula: z^2/c^2+1=x^2/a^2+y^2/b^2

>	implicitplot3d(z^2+1=x^2+y^2,x=-2.5..2.5,y=-2.5..2.5,z=-2..2,grid=[19,19,19],orientation=[50,80]);

>

Hyperboloid of Two Sheets

Elemenary example: z^2-1=x^2+y^2

More General Formula: z^2/c^2-1=x^2/a^2+y^2/b^2

>	implicitplot3d(z^2-1=x^2+y^2,x=-3..3,y=-3..3,z=-3..3,grid=[19,19,19],orientation=[50,80]);

>

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