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Find the equation of the chord joining the points (x1, y1) and (x2, y2) lying on the rectangular hyperbola xy = c².

1. x/(x1 + x2) + y/(y1 + y2) = 1
2. x/(x1 - x2) + y/(y1 - y2) = 1
3. x/(y1 + y2) + y/(x1 + x2) = 1
4. x/(y1 - y2) + y/(x1 - x2) = 1

Correct answer: x/(x1 + x2) + y/(y1 + y2) = 1

Solution

Using the parametric chord x + t1 t2 y = c(t1 + t2) and substituting x1+x2 = c(t1+t2), y1+y2 = c(1/t1 + 1/t2), it rearranges to x/(x1+x2) + y/(y1+y2) = 1.

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