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  • If tangents OQ and OR are drawn to variable circles having radius r and the centre lying on the rectangular hyperbola xy=1 , then the focus of the circumcentre of triangle OQR i

If tangents OQ and OR are drawn to variable circles having radius

r and the centre lying on the rectangular hyperbola xy=1 , then

the focus of the circumcentre of triangle OQR is (O being the 

origin)

Option: 1

xy=4


Option: 2

xy=1/4


Option: 3

xy=1


Option: 4

None of these


Answers (1)

best_answer

Let S be the point on the rectangular hyperbola [say (t,1/t)].

Now, the circumcircle of  \mathrm{\triangle OQR} also passes through S.

Therefore, the circumcenter is the midpoint of OS. Hence,

\mathrm{x=\frac{t}{2}, y=\frac{1}{2 t}}

So, the focus of the circumcenter is xy=1/4.

Posted by

Ritika Jonwal

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