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Consider the curves given by x³ - 3xy² + 2 = 0 and 3x²y - y³ = 2. How do these two curves intersect?

1. They intersect orthogonally
2. They are tangent to each other
3. They intersect at an angle of π/3
4. They intersect at an angle of π/4

Correct answer: They intersect orthogonally

Solution

The curves intersect orthogonally when their tangent lines at the points of intersection are perpendicular to each other, which occurs when the product of their slopes is -1. This condition is satisfied for the given curves, indicating that they cross at right angles.

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