Definition:Conchoid of Nicomedes

Definition
The conchoid of Nicomedes is the plane curve defined in Cartesian coordinates as:
 * $\left({x - a}\right)^2 \left({x^2 + y^2}\right) = b^2 x^2$

or in polar coordinates as:
 * $r = b + a \sec \theta$

for some real constants $a \in \R$, $b \in \R_{> 0}$.


 * ConchoidOfNicomedes.png

The above diagram illustrates the conchoid of Nicomedes for $b = 1$ and various values of $a$ from $0$ to $3$.

Also known as
Some sources suggest that the conchoid of Nicomedes can also be referred to as a cochloid. However, this usage can be confused easily with the cochleoid which some dictionaries give cochloid as an alternative for.

Others refer to it as merely a conchoid, but that term is best used to refer to the more general object of which the conchoid of Nicomedes is an example.