Jacobian Curve

The Jacobian of a linear net of curves of order $n$ is a curve of order $3(n-1)$. It passes through all points common to all curves of the net. It is the Locus of points where the curves of the net touch one another and of singular points of the curve.

See also Cayleyian Curve, Hessian Covariant, Steinerian Curve

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 149, 1959.