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A conic satisfies the differential equation x dy + y dx = 0 and passes through the point (2, 8). Find the length of its latus rectum.
- 4*sqrt(2)
- 8
- 8*sqrt(2)
- 16
Correct answer: 8*sqrt(2)
Solution
The curve is xy = 16 = c² with c = 4; a rectangular hyperbola has latus rectum = transverse axis = 2*sqrt(2)*c = 8*sqrt(2).
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