Let $Y$ be the affine plane curve given by the equation $y^2=F(x)$, where $F$ is a polynomial in one variable of odd degree over a field of characteristic not equal to 2. Let $\xi\in Y$.
- Suppose $y(\xi)\neq0$. Then why is $x$ a local parameter at $\xi$?
- Suppose $y(\xi)=0$. Then why is $y$ a local parameter at $\xi$?