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Question

A circle cuts the rectangular hyperbola xy=1 in points (xr,yr), r=1,2,3,4 then

A
x1x2x3x4=1
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B
x1x2+x3x4=1
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C
x1x2x3x4=1
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D
x1+x2+x3+x4=0
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Solution

The correct option is C x1x2x3x4=1
Let the circle is x2+y2+2gx+2fy+c=0
So for point of intersection of circle and given hyperbola
x2+1x2+2gx+2fx+c=0
x4+2gx3+cx2+2fx+1=0
Sum of roots =x1+x2+x3+x4=2g
Products of roots =x1x2x3x4=1
Hence, option 'C' is correct.

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