The two curves xt-3xy2+2=0 and 3x2y-y3=2

Two curves cuts at right angle if product of their slopes  is -1 .  Two given curves are x3-3xy2+2=0----------(1) and 3x2y-y3-2=0---------(2) Differentiate equ. (i), ⇒m1=dydx=3x2-y26xy Differentiate equ. (ii), ⇒m2=dydx=-2xyx2-y2∴m1×m2=x2-y22xy×-2xyx2-y2⇒m1×m2=-1