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If the hyperbola xy=c^(2) intersects the...

If the hyperbola `xy=c^(2)` intersects the circle `x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4))` then show that
(i) `x_(1)+x_(2)+x_(3)+x_(4)=0`
(ii) `y_(1)+y_(2)+y_(3)+y_(4)=0`
(iii) `x_(1)x_(2)x_(3)x_(4)=c^(4)`
(iv) `y_(1)y_(2)y_(3)y_(4)=c^(4)`

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