Fix a plane algebraic curve in real 2-space, a point P in 2-space, and a positive real number d. Associated to this data is a conchoid.

This is the set of points Q in R2 such that

  1. the line through P and Q intersects the curve
  2. the intersection point is distance d from Q.

For examples see conchoid of Nicomedes, conchoid of de Sluze.