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 Cx1x2x3x4=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.