Which of the following ringed spaces are isomorphic over $\mathbb{C}$?
(a) $\mathbb{A}^1\backslash\{1\}$
(b) $V(x_1^2+x_2^2)\subset \mathbb{A}^2$
(c) $V(x_2-x_1^2, x_3-x_1^3)\backslash \{0\} \subset \mathbb{A}^3$
(d) $V(x_1x_2)\subset \mathbb{A}^2$
(e) $V(x_2^2-x_1^3-x_1^2)\subset \mathbb{A}^2$
(f) $V(x_1^2-x_2^2-1)\subset \mathbb{A}^2$
I think (a) and (c) are isomorphic, since in (c), $V(x_2-x_1^2, x_3-x_1^3)$ can be mapped to $\{(t,t^2,t^3):t\in \mathbb{C}\}$.
(b) and (d) are isomorphic, since they are both essentially two lines, considered over $\mathbb{C}$. Is (f) also isomorphic to (b) and (d)? (f) is a pair of hyperpola in $\mathbb{R^2}$. Could it be mapped to the two lines using isomorphism?
I couldn't see anything else. My other question is, is there a better, typical way to answer this kind of questions? Thank you for your help!