A similar derivation show that, conversely, any hyperbola is the cissoid of two non-parallel lines relative to any point on it. Cissoids of Zahradnik A cissoid of Zahradnik (named after Karel Zahradnik) is defined as the cissoid of a conic section and a line relative to any point on the conic. This is a broad family of rational cubic curves containing several well-known examples. Specifically: The Trisectrix of Maclaurin given by is the cissoid of the circle and the line relative to the origin. The right strophoid is the cissoid of the circle and the line relative to the origin. The cissoid of Diocles is the cissoid of the circle and the line relative to the origin. This is, in fact, the curve for which the family is named and some authors refer to this as simply as cissoid. The cissoid of the circle and the line where is a parameter, is called a Conchoid of de Sluze. (These curves are not actually conchoids.) This family includes the previous examples. The folium of Descartes is the cissoid of the ellipse and the line relative to the origin. To see this, note that the line can be written and the ellipse can be written So the cissoid is given by which is a parametric form of the folium. See also Conchoid Strophoid References C. A. Nelson "Note on rational plane cubics" Bull. Amer. Math. Soc. Volume 32, Number 1 (1926), 71-76. External links 2D Curves Curves Algebraic curves zh:蔓叶线