Zariski closure of the curve $P_\alpha=0$ in the chart $(1/X,1/Y)$ of $\mathbb P^1\times\mathbb P^1$

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Zariski closure of the curve $P_\alpha=0$ in the chart $(1/X,1/Y)$ of $\mathbb P^1\times\mathbb P^1$ · Prove2Me