From the point \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}, ...

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From the point \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \), tangents are
P drawn to the rectangular hyperbola \( x y=c^{2} \). If the

W. conic passing through the two given points and the four points of contact is a circle, then show that \( x_{1} x_{2}=y_{1} y_{2} \) and \( x_{1} y_{2}+x_{2} y_{1}=4 c^{2} \).
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