I'm not really sure what needs to be done here: Prove that if Q(x0,y0) is any point whose coordinates x0, y0 are non-zero, then there is a unique hyperbola passing through the point Q whose asymptotes are the coordinate axes x and y.
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Hint: Investigate $\displaystyle xy = x_0 y_0$.
Do you mind elaborating a little bit? I'm not quite sure what that means.
Posting in multiple locations really is discouraged. Using volunteers responses without proper credit on other sites really is doscouraged. Are you getting anywhere on that uniqueness?
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