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 the curve passes through the origin and write "y"="mx". Then "f" can be written If "b"+"mb" is not 0 then "f"=0 has a solution of multiplicity 1 at "x"=0 and the origin is a point of single contact with line "y"="mx". If "b"+"mb"=0 then "f"=0 has a solution of multiplicity 2 or higher and the line "y"="mx", or "b"x+"b"y=0, is tangent to the curve. In this case, if "c"+2"mc"+c"m" is not 0 then the curve has a point of double contact with "y"="mx". If the coefficient of "x", "c"+2"mc"+c"m", is 0 but the coefficient of "x" is not then the