Fix a
plane algebraic curve in
real 2space, a
point
P in 2space, and a positive real number
d. Associated to
this data is a
conchoid.
This is the set of points Q
in R^{2} such that

the line through P and Q intersects the curve

the intersection point is distance d from Q.
For examples see conchoid of Nicomedes, conchoid of de Sluze.