Let $K := (uw - v^2, w^3 - u^5)$. Show that $V(K)$ consists of two irreducible components, one of which is $V(uw - v^2, w^3 - u^5, u^3-vw) = V(J)$.
I don't know how to start this. I see that $V(K)$ is symmetric under the interchange of $v \to -v$ but that $V(J)$ isn't. Does this mean that the other component should be symmetric under this exchange?