Let $F$ be an algebraically closed field, and consider the ring $F[X, Y]$ of polynomials over $F$ in two indeterminates $X$ and $Y$. Let $S$ be the multiplicatively closed set in $F[X, Y]$ generated by polynomials of the form $X−α$ and $Y−β$ for all non-zero elements $α, β \in F$, and set $R=S^{-1}F[X,Y]$ a Noetherian domain of Krull dimension two. The only non-principal maximal ideal of $R$ is $M=S^{-1}(X,Y)$, while $R$ has infinitely many principal (height one) maximal ideals.

Why The only non-principal maximal ideal of $R$ is $M=S^{-1} (X,Y)$?

why $R$ has infinitely many principal (height one) maximal ideals?