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Find the length of the latus rectum of the conic defined by the equation x*y = 7x + 5y.

1. sqrt(280)
2. sqrt(225)
3. sqrt(180)
4. sqrt(325)

Correct answer: sqrt(280)

Solution

The equation factors to (x-5)(y-7) = 35, a rectangular hyperbola with c² = 35. After a 45-degree rotation the standard form is u² - v² = 70, giving a = sqrt(70). The latus rectum of a rectangular hyperbola equals 2a = 2*sqrt(70) = sqrt(280).

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