Cissoid

Given two curves $C_1$ and $C_2$ and a fixed point $O$, let a line from $O$ cut $C_1$ at $Q$ and $C_2$ at $R$. Then the Locus of a point $P$ such that $OP = QR$ is the cissoid. The word cissoid means ``ivy shaped.''

Curve 1	Curve 2	Pole	Cissoid
Line	Parallel Line	any point	line
Line	Circle	center	Conchoid of Nicomedes
Circle	tangent line	on Circumference	oblique cissoid
Circle	tangent line	on Circumference opp. tangent	Cissoid of Diocles
Circle	radial line	on Circumference	strophoid
Circle	concentric Circle	center	Circle
Circle	same Circle	$(a\sqrt{2}, 0)$	Lemniscate

See also Cissoid of Diocles

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 53-56 and 205, 1972.

Lee, X. ``Cissoid.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Cissoid_dir/cissoid.html.

Lockwood, E. H. ``Cissoids.'' Ch. 15 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 130-133, 1967.

Yates, R. C. ``Cissoid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 26-30, 1952.