Working out some questions from Ravi Vakil's notes. Here is a question:
Question: Suppose $\operatorname{char}\bar{k} \neq 2$ and let $C$ be the curve defined by $x^{2}+y^{2} = z^{2}$. Let $\rho$ be the projection $C \to \mathbb{P}^{1}$ given by $(x:y:z) \to (x:y)$. If $p$ is a point in $\mathbb{P}^{1}$, how many points does $\rho^{-1}p$ have?
Would be grateful if you help.