Conchoids of Nicomedes
Draw different conchoids with different pens on the same moving plane

The Concoid is over 2000 years old. It was geometrically defined, formulas came much later. We use this parametrization:
  c(t) = RR * [ tan(t) + k*sin(t), 1 + k•cos(t) ]
The parameter k specifies different pen positions on the same drawing mechanism. The drawing mecahnism is a line through the origin with a fixed point P on this line (big yellow dot) moving on the yellow line, called "directrix" of the conchoid. k is the (signed) distance from P to the drawing pen (big magenta dot) on the moving line.