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Let the center $B$ of a Circle of Radius $a$ move along a line $BA$. Let $O$ be a fixed point located a distance $c$ away from $AB$. Draw a Secant Line through $O$ and $D$, the Midpoint of the chord cut from the line $DE$ (which is parallel to $AB$) and a distance $b$ away. Then the Locus of the points of intersection of $OD$ and the Circle $P_1$ and $P_2$ is called a kieroid.

Special Case Curve
$b=0$ Conchoid of Nicomedes
$b=a$ Cissoid plus asymptote
$b=a=-c$ Strophoid plus Asymptote


Yates, R. C. ``Kieroid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 141-142, 1952.

© 1996-9 Eric W. Weisstein