Cartesian equation of a surface

Question

Given the following surface $$\sigma(u,v)=(\cos u,2\sin u,v)$$ I gotta find a cartesian equation of it. What I could conclude was $$4x^2+y^2=4$$ Is there a way to associate $x$ and $y$ with $z$?

Answer 1

Because $z=v$ is independent of the other coordinates, your surface is the cylinder, aligned with the $z$-axis, with $4x^{2}+y^{2}=4$ as its cross section. (So in this case, it is an elliptical cylinder.)