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If the curves x²/a + y²/b = 1 and x²/c + y²/d = 1 cut each other orthogonally (at 90 deg), which relation must hold?

1. a - b = c - d
2. a + b = c + d
3. a - c = b + d
4. ab = (c + d)/(a + b)

Correct answer: a - b = c - d

Solution

Differentiating both conics and imposing that the tangent slopes multiply to -1 at the common point yields the condition a - b = c - d.

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