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$F=y^2-x^2-x^3$

We have find the singularities of the function, the folds and the equations of the tangent lines.

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It is a cubic curve, so it has at most $\;\dfrac{(3-1)(-3-2)}2=1$ singular point. Now the origin is an ordinary double point and the two tangents have equation $$x^2-y^2=0.$$

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