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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 `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 which of the following need not hold.
(a)  `x_1+x_2+x_3+x_4=0`
(b)  `x_1 x_2 x_3 x_4=y_1 y_2 y_3 y_4=c^4`
(c)  `y_1+y_2+y_3+y_4=0`
(d)  `x_1+y_2+x_3+y_4=0`

A

`x_(1)+x_(2)+x_(3)+x_(4)=0`

B

`x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=c^(4)`

C

`y_(1)+y_(2)+y_(3)+y_(4)=0`

D

`x_(1)+y_(2)+x_(3)+y_(4)=0`

Text Solution

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The correct Answer is:
D
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