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If the circle x^2+y^2=a^2 intersects the...

If the circle `x^2+y^2=a^2` intersects the hyperbola `x y=c^2` at four points `P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3),` and `S(x_4, y_4),` then `x_1+x_2+x_3+x_4=0` `y_1+y_2+y_3+y_4=0` `x_1x_2x_3x_4=C^4` `y_1y_2y_3y_4=C^4`

A

`Sigmax_(i) =0`

B

`Sigmay_(i) = 0`

C

`x_(1)x_(2)x_(3)x_(4) = C^(4)`

D

`y_(1)y_(2)y_(3)y_(4) = C^(4)`

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