Consider the parametrization of a surface: $$r = \langle u \text{ cos}(v), u^2 \text{ cos}(2v), u \text{ sin}(v) \rangle$$ The question asks to find surface $S$. I'm new learning calculus $3$ and having trouble to approach this question.
Any hint or suggestion would be really appreciate.
Note
$$y=u^2\cos 2 v = u^2(\cos^2v-\sin^2v)=x^2-z^2$$