Trident Curve

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In mathematics, a **trident curve** (also **trident of Newton** or **parabola of Descartes**) is any member of the family of curves that have the formula:

Trident curves are cubic plane curves with an ordinary double point in the real projective plane at*x* = 0, *y* = 1, *z* = 0; if we substitute *x* = *x*/*z* and *y* = 1/*z* into the equation of the trident curve, we get

which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.

## References

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- <math>xy+ax^3+bx^2+cx=d,</math>

Trident curves are cubic plane curves with an ordinary double point in the real projective plane at

- <math>ax^3+bx^2z+cxz^2+xz = dz^3,,</math>

which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.

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