View source for Nicomedes conchoid

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A plane [[Algebraic curve|algebraic curve]] of order 4 whose equation in Cartesian rectangular coordinates has the form

$$(x^2+y^2)(x-a)^2-l^2x^2=0;$$

and in polar coordinates

$$\rho=\frac{a}{\sin\psi}\pm l.$$

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/n066620a.gif" />

Figure: n066620a

Outer branch (see Fig.). Asymptote $x=a$. Two points of inflection, $B$ and $C$.

Inner branch. Asymptote $x=a$. The coordinate origin is a double point whose character depends on the values of $a$ and $l$. For $l<a$ it is an isolated point and, in addition, the curve has two points of inflection, $E$ and $F$; for $l>a$ it is a [[Node|node]]; for $l=a$ it is a [[Cusp(2)|cusp]]. The curve is a [[Conchoid|conchoid]] of the straight line $x=a$.

The curve is named after Nicomedes (3rd century B.C.), who used it to solve the problem of trisecting an angle.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,   "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,   "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>