$R = k[x,y,z,w,u]/(xw-z^5 +y^9, y^2u-4x^9-z^2)$, where $k$ is field of characteristic $0$. Then i know that $R$ is not a normal ring, $\dim (R) = 3$.
My question is:
Is $R_x \cap R_y$ affine?
I tried Macaulay2 but it doesn't localize quotient rings. Any help would be appreciated. Thank you!