The two curves x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of

Given the curve x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0

x³ – 3xy² + 2 = 0

Differentiating on both sides with respect to x, we get

Applying the sum rule of differentiation and also the derivative of the constant is 0, so we get

Applying the power rule we get

Now applying the product rule of differentiation, we get

Let this be equal to m₁

3x²y – y³ – 2 = 0

Differentiating on both sides with respect to x, we get

Applying the sum rule of differentiation and also the derivative of the constant is 0, so we get

Applying the power rule we get

Now applying the product rule of differentiation, we get

Let this be equal to m₂

Multiplying equation (i) and (ii), we get

⇒ m₁.m₂=-1

As the product of the slopes is -1, hence both the given curves are intersecting at right angle i.., they are making angle with each other.

So the correct option is option C