The point O is called the pole. The given line is called its directrix, and is an asymptote. The following figures shows the curve family. The figure on the left has constants k from -2 to 2. The right has constants k from -100 to 100.
Formulas Let the distance between pole and line be b, and the given constant be k.
Also, for a given k, the curve has two branches. In a math context, it would be better to define the curve with a signed constant k corresponding to a curve of only one branch. We will be using this intepretation of k. In this respect, the conchoid of Nichomedes is then two conchoids of a line with constants k and -k. Curves with positive offsets are always smooth.