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Question

Locus of a point, whose chord of contact with respect to the circle x2+y2=4 is a tangent to hyperbola xy=1 is :

A
xy=4
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B
x2y2=6
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C
xy=8
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D
x2y2=16
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Solution

The correct option is A xy=4
Let point be P(h,k)
chord of contact of from P to x2+y2=4 is
hx+ky=4(1)
(1) is tangent to xy=1
So solving equation (1) with xy=1, we have
x(4hxk)=1
4xhx2=k
hx24x+k=0
Discrimant of the above equation must be zero for the equation to touch at one point.
164hk=0
xy=4
Hence, locus is a rectangular hyperbola.

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