Consider the subset $X:=\{(t^{2},t^{3})|t\in\mathbb{C}\}$ in $\mathbb{C}^{2}$, and set $X_{0}:=X\backslash\{(0,0)\}$. Show that $$\mathcal{V}(\mathcal{J}(X_{0}))=X.$$Note: here $\mathcal{V},\mathcal{J}$ stand for the common zero locus and vanishing ideal functions, respectively.
Could you please give me a hint as to what to do? This is my first time actually working with algebraic varieties, and I'm not sure where to start.