The question is this:
Let $f:\mathbb C[x,y]\rightarrow\mathbb C[t]$ be the homomorphism that sends $x\mapsto t+1$ and $y\mapsto t^3-1.$ Determine the kernel $K$ of $f$, and prove that every ideal $I$ of $\mathbb C[x,y]$ that contains $K$ can be generated by two elements.
Solution:
I have shown that $((x-1)^3-y-1)=K.$ However, I am having trouble showing the second part. Any hints??