I would like to find affine cover of blow-up $X = Bl_{I} \mathbb A^2$, where $I=(x^3, xy, y^2)$. I know that $X=\{((x_1, x_2),[y_1,y_2,y_3])\subset \mathbb A^2\times\mathbb P^2: x_1^3y_2=x_1x_2y_1, x_1^3y_3=x_2^2y_1, x_1x_2y_3=x_2^2y_2 \}$. I've tried to use standard cover, i.e. $X\cap (\mathbb A^2\times U_i)$. I don't know how to see what is it.
Thank you in advance.