The asymptotes of xy = hx + ky are

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x = h, y = k

x = –h, y = –k

x = k, y = h

x = –k, y = –h

answer is C.

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Detailed Solution

Equation of the asymptotes differ from the equation of the hyperbola by a constant so the equation of the asymptotes is xy−hx−ky+λ=0 which represents a pair of lines if λ=hk and the required asymptotes are x=k and y=h.

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