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6.If the circle x^(2)+y^(2)=a^(2) inters...

6.If the circle `x^(2)+y^(2)=a^(2)` intersects the hyperbola` xy=c^(2) `in four points P`(x_(1) y_(1)) ``Q(x_(2) y_(2))`` R(x_(3) y_(3))` `S(x_(4) y_(4))` then 1) `x_(1)+x_(2)+x_(3)+x_(4)=2c^(2)`` 2) y_(1)+y_(2)+y_(3)+y_(4)=0`` 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) ``4) y_(1)y_(2)y_(3)y_(4)=2c^(4) `

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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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