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If tangents `O Q` and `O R` are dawn to variable circles having radius `r` and the center lying on the rectangular hyperbola `x y=1` , then the locus of the circumcenter of triangle `O Q R` is `(O` being the origin). (a) `x y=4` (b) `x y=1/4` `x y=1` (d) none of these

A

xy = 4

B

xy = 1/4

C

xy = 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let S be a point on the rectangular hyperbola [say (t,1/t)].
Now, the circumcircle of `Delta`OQR also passes through S.

Therefore, the circumcenter is the midpoint of OS. Hence,
`x=(t)/(2),y=(1)/(2t)`
So, the locus of the circumcenter is `xy=1//4`.
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