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The equation of the chord joining two points \( \left(x_{1}, y_{1}\right) \)
\( \mathrm{P} \) and \( \left(x_{2}, y_{2}\right) \) on the rectangular hyperbola \( x y=c^{2} \) is

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(1) \( \frac{x}{x_{1}+x_{2}}+\frac{y}{y_{1}+y_{2}}=1 \)
(2) \( \frac{x}{x_{1}-x_{2}}+\frac{y}{y_{1}-y_{2}}=1 \)
(3) \( \frac{x}{y_{1}+y_{2}}+\frac{y}{x_{1}+x_{2}}=1 \)
(4) \( \frac{x}{y_{1}-y_{2}}+\frac{y}{x_{1}-x_{2}}=1 \)
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