STROPHOID L0G0CYCLIC

CURVE  or FOLIATE, a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line . The polar equation is rcosO =a(r t sing), the upper sign referring to the case when the vector is increased, the lower when it is diminished . Both branches are included in the Cartesian equation (x2+y2) (2a—x) =a2x, where a is the distance of the line from the origin . If we take for axes the fixed line and the perpendicular through the initial point, the equation takes the form y sl (a—x) =x Al (a+x) . The curve resembles the folium of Descartes, and has a node between x = o, x = a, and two branches asymptotic to the line x=-- 2a .