I just have not gotten the gist of parametric curves yet. I don't quite understand how to go from a vector $R(u,t)$ to an equation or vice-versa. So, if you guys could help me with the following:
Identify the surface $r(u, v) = \langle\sqrt{v} \sin(u), v\cos^2(u), \sqrt{v})\rangle$.
This stuff is immensely hard for me, so please go lightly (I'm new here!). Thanks all.
We have $x^2+y=v\sin^2 u+v\cos^2 u=v=z^2$. This is an equation of a hyperbolic paraboloid.