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Question

If the circle x2+y2=a2 intersects the hyperbola xy=c2 in four points P(x1,y1),Q(x2,y2),R(x3,y3),S(x4,y4), then which of the following need not hold

A

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B

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C

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D

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Solution

The correct option is D

The abscissae of the points of intersection of the given curves are connected by
x2+c4x2=a2x4a2x2+c4=0
As x1,x2,x3,x4 are the roots of this equation x1+x2+x3+x4 =0,x1x2x3x4=c4
Similarly y1+y2+y3+y4=0,y1y2y3y4=c4

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