Cylinders and Quadric Surfaces: Examples

1. What type of surface is : 4*x^2-3*y^2+12*z^2+12=0?

Anwser:

First solve for z:

>	solve(4*x^2-3*y^2+12*z^2+12=0,z);

Then grpah:

>	plot3d([1/6*(-12*x^2+9*y^2-36)^(1/2), -1/6*(-12*x^2+9*y^2-36)^(1/2)],x=-10..10,y=-10..10)

2. What type of surface is : x^2+2*y^2+z^2-4*x+4*y-2*z+3=0?

Anwser:

First solve for z:

>	solve(x^2+2*y^2+z^2-4*x+4*y-2*z+3=0,z);

Then grpah:

>	plot3d([1+(-2-x^2-2*y^2+4*x-4*y)^(1/2), 1-(-2-x^2-2*y^2+4*x-4*y)^(1/2)],x=-4..4,y=-4..4);