Let $X=\{(t^4,t^5,t^6,t^7)\in k^4, t \in k\}$, $Y=\{(t,t^2,t^3,t^4)\in k^4, t \in k\}$
Obviously $Y=V(y-x^2,z-x^3,w-x^4)$, and also $X$ seems to be $X=V(y^4-x^5,xz-y^2,yw-z^2)$.
Is $X$ right? I'm quite not sure, since there can be similar things $z^4-x^6, w^4-x^7$ etc..
What's the difference between $X$ and $Y$?