Q.

If a circles x2+y2=a2 and the  rectangular hyperbola xy=c2 intersect in four points, ctr,ctr , r=1,2,3,4 then t1t2t3t4 is equal to

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a

-1

b

1

c

c4

d

-c4

answer is B.

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Detailed Solution

Parametric equation of the hyperbola xy=c2  is ct,ctsubstitute this point in the circle x2+y2=a2c2t4−a2t2+c2=0 for which t1,t2,t3,t4 are rootsHence, t1t2t3t4=product of roots=c2c2=1
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If a circles x2+y2=a2 and the  rectangular hyperbola xy=c2 intersect in four points, ctr,ctr , r=1,2,3,4 then t1t2t3t4 is equal to