Implicit representations of a parametric surface

Hello,

I was just wondering what are the steps taken to derive an implicit representation of a surface(i.e f(x,y,z)=constant).

the example in my text book says the Elliptic Paraboloid r(s,t)=3scost**i** +4ssint**j** +s^2**k** has implicit representation z=x^2/9 +y^2/16.

But how do i get to this? Am i just meant to know what the general equation of each surface is in both forms and figure it out from there?

As much help as possible would be great.

thanks for all the help you guys have given me so far.