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Question

# If the circle x2+y2=a2 intersects the hyperbola xy=c2 at four points P(x1,y1),Q(x2,y2),R(x3,y3), and S(x4,y4), then

A
x1+x2+x3+x4=0
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B
y1+y2+y3+y4=0
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C
x1x2x3x4=c4
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D
y1y2y3y4=c4
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Solution

## The correct options are A x1+x2+x3+x4=0 B y1+y2+y3+y4=0 C x1x2x3x4=c4 D y1y2y3y4=c4Putting y=c2x in x2+y2=a2, we get x2+c4x2=a2or x4−a2x2+c4=0As x1,x2,x3, and x4 are the roots of (i), we have x1+x2+x3+x4=0 and x1x2x3x4=c4 Similarly, forming equation in y, we get y1+y2+y3+y4=0 and y1y2y3y4=c4

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