\begin{definition}[Definition:Conchoid of Nicomedes]
The '''conchoid of Nicomedes''' is the plane curve defined in Cartesian coordinates as:
:$\paren {x - a}^2 \paren {x^2 + y^2} = b^2 x^2$
or in polar coordinates as:
:$r = b + a \sec \theta$
for some real constants $a \in \R$, $b \in \R_{> 0}$.
:600px
The above diagram illustrates the '''conchoid of Nicomedes''' for $b = 1$ and various values of $a$ from $0$ to $3$.
\end{definition}