Trident of Newton

The Cubic Curve defined by

$$ax^3+bx^2+cx+d=xy$$

with $a\not=0$. The curve cuts the axis in either one or three points. It was the 66th curve in Newton's classification of Cubics. Newton stated that the curve has four infinite legs and that the $y$-axis is an Asymptote to two tending toward contrary parts.

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 109-110, 1972.

MacTutor History of Mathematics Archive. ``Trident of Newton.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Trident.html.