Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
Singular point of a curve smooth function "h" so that the curve has the form "y"="h"("x") near the origin. Similarly, if "b"≠0 then there is a smooth function "k" so that the curve has the form "x"="k"("y") near the origin. In either case, there is a smooth map from R to the plane which defines the curve in the neighborhood of the origin. Note that at the origin so the curve is non-singular or "regular" at the origin if at least one of the partial derivatives of "f" is non-zero. The singular points are those points on the curve where both partial derivatives vanish, Assume