The Kappa Curve as a Locus
The kappa curve looks vaguely like a curly kappa, , and was studied by Newton, Bernoulli, and Gutschoven. Sometimes called Gutschoven's curve, its double cusp form can be represented as .[more]
Let be the point (magenta). Let be the intersection point (blue) of the horizontal line with a line rotating about the origin . The kappa curve is the locus of points (red) on the rotating line such that distances (green segments).[less]
 T. Heard, D. Martin, and B. Murphy, A2 Further Pure Mathematics, 3rd ed., London: Hodder Education, 2005 p. 209, question 13.