Answer :

If the two curve cut orthogonally then angle between their tangent at intersecting point is equal to 90⁰.

We have to find their intersecting point.


x3 – 3xy2 + 2 = 0 …(1) and 3x2y – y3 – 2 = 0 …(2)


On adding eq (1) and eq (2)


x3 – 3xy2 + 2 + 3x2y – y3 – 2 = 0


x3 – y3 – 3xy2 + 3x2y = 0


(x – y)3 = 0 x = y


Put x = y in eq (1)


y3 – 3y3 + 2 = 0 y = 1


At y = 1, x = 1



m1 at (1, 1) = 0



m2 at (1, 1) = -2/0


At (1, 1)





So, we can say that two curve cut each other orthogonally because angle between two tangent at their intersecting point is equal to 90⁰.


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