If the circle \( x^{2}+y^{2}=a^{2} \) intersects the hyperbola \( x...

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If the circle \( x^{2}+y^{2}=a^{2} \) intersects the hyperbola \( x y=c^{2} \) at
P four points \( P\left(x_{1}, y_{1}\right), Q\left(x_{2}, y_{2}\right), R\left(x_{3}, y_{3}\right) \), and \( S\left(x_{4}, y_{4}\right) \), then
W
(1) \( x_{1}+x_{2}+x_{3}+x_{4}=0 \)
(2) \( y_{1}+y_{2}+y_{3}+y_{4}=0 \)
(3) \( x_{1} x_{2} x_{3} x_{4}=c^{4} \)
(4) \( y_{1} y_{2} y_{3} y_{4}=c^{4} \)
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