View source for Conchoid

''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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244201.png" />. If the equation of the given curve is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244202.png" /> in polar coordinates, then the equation of its conchoid has the form: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244203.png" />. Examples: the conchoid of a straight line is called the [[Nicomedes conchoid|Nicomedes conchoid]]; the conchoid of a circle is called the [[Pascal limaçon|Pascal limaçon]].



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====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>