5 typesNewtons Classification of third-order curves9 types2 types12 types9 types2 types3 types4 types6 types7 types7 types4 typesClass VIICanonical form Dy = + + cx + dCubic ParabolaClass VICanonical form C= + cx + dDiverging ParabolaClass VCanonical form Bxy = + + cx + dTrident( c = 0 )Adiametric( c 0 )MonodiametricCanonical form A+ ey = +cx + d(e 0 )Adiametrice = 0, 4ac, b 0Monodiametrice = 0, = 4ac, b 0Tridiametricb = 0With asymptotes intersect in one pointC = 0Parabolic hyperbolism( c < 0 )Elipric hyperbolism(c > 0 )Hyperbolic hyperbolism( c 0 )Monodiametric( c = 0 )AdiametricClass I(a > 0 )Hyperbolic hyperbolaClass II( a < 0 )Defective hyperbolaClass III( a = 0, b 0)Parabolic hyperbolaClass IV(a = b = 0 )Conical section hyperbolism