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.