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Which of the following pairs of curves are orthogonal to each other (intersect at right angles at every point of intersection)?

1. y = |x| and y = 3 - |x|
2. x²/3 + y² = 1 and x² - y² = 3
3. x*y = 1 and x² - y² = 3
4. y² = 4x and x² = 8y

Correct answer: x*y = 1 and x² - y² = 3

Solution

For the pair xy=1 and x²-y²=3, differentiating xy=1 gives slope m1=-y/x and differentiating x²-y²=3 gives slope m2=x/y. Their product m1*m2 = -1 everywhere, confirming orthogonality. The other options can be checked to fail this condition.

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