Conchoid

2020 Mathematics Subject Classification: Primary: 53A04 [MSN][ZBL]

of a curve

The planar curve obtained by increasing or decreasing the position vector of each point of a given planar curve by a segment of constant length $l$. If the equation of the given curve is $\rho=f(\phi)$ in polar coordinates, then the equation of its conchoid has the form: $\rho=f(\phi)\pm l$.

Examples: the conchoid of a straight line is called the Nicomedes conchoid; the conchoid of a circle is called the Pascal limaçon.

References

[a1]	J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) Zbl 0257.50002