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Find the locus of the midpoints of a system of parallel chords of slope m of the rectangular hyperbola xy = c².
- y + mx = 0
- y - mx = 0
- my - x = 0
- my + x = 0
Correct answer: y + mx = 0
Solution
The chord with midpoint (h, k) has slope -k/h, so m = -k/h gives k + m h = 0, i.e. y + mx = 0.
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