In this paper we geometrically provide a necessary and sufficient condition for points on a cubic to be associated with an infinite family of other cubics who have nine-pointic contact at that point. We then provide a parameterization of the family of cubics with nine-pointic contact at that point, based on the osculating quadratic.
Prof. Seth Dutter, Department of Mathematics Statistics and Computer Science, University of Wisconsin-Stout
Balay-Wilson, Leah and Brysiewicz, Taylor
"Points of Ninth Order on Cubic Curves,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss1/1