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I consider the hypersurface $Y = V(y(x^2+z^2)-x) \subset \mathbb{A}^3_k$ ($k = \mathbb{C}$)

I've read that if you have two skew lines on a non-singular cubic surface $Y$, given by a polynomial of degree 3, then you can find a rational map to a plane.

To find a parametrization of $Y$, first i need to find two skew lines lying on $Y$. How can i find them?

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