differential geometry help

I'm not sure this is the right forum, I hope the moderator will move it if necessary.

(1) I have to sketch level sets $\displaystyle f^{-1}(c)$, c=1, 0, -1, for the function $\displaystyle f(x_1, x_2, x_3)=x_1 x_2 -x_3^2$

I know level sets are $\displaystyle \{(x_1, x_2, x_3) | x_1 x_2 -x_3^2=1, 0, -1\}$ but how do i sketch this? :(

(2) Let $\displaystyle \phi:\mathbb{R}^3 \rightarrow S^3$ be the inverse of stereographic projection from $\displaystyle S^3-\{(0, 0, 0, 1)\}$ to the equatorial hiperplane $\displaystyle x_4=0$. Show that for every vector $\displaystyle p \in \mathbb{R}^3$ exists $\displaystyle \lambda(p) \in \mathbb{R}^3$ such that

$\displaystyle ||d\phi(v)||= \lambda (p) ||v||, \forall v \in {\mathbb{R}^3}_p$.

I don't even know how to start..

Thank you for your time and help!