(generalized) conchoid


with h(t) = √(f2(t)+g2(t))

Given a curve C1(f(t), g(t)) and a fixed point O(0,0). Draw lines l through O that intersect C1 in Q. Then the conchoid is defined as the collection of points P (on l) for which PQ is equal to a constant a.

This conchoid is a generalization of the 1st curve that was named as a conchoid, the (simple) conchoid that is derived from the straight line.



In the following table some conchoids have been collected:
C1 O conchoid of C1
Archimedes' spiral center Archimedes' spiral
circle on C1 limaçon 
When the constant a is equal to the diameter of C1 the cardioid appears.
  not on C1 conchoid of a circle
curve with polar equation r = f(φ) the origin curve with polar equation r = f(φ) + a
rose center botanic curve
straight line  

(simple) conchoid

The conchoid of Dürer does not belong to this family, it is another variation on the conchoid.