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Question

PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy=8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1,1) to director circle of the conic is


Your Answer
A
3 unit
Correct Answer
B
2 unit
Your Answer
C
23 unit
Your Answer
D
25 unit

Solution

The correct option is A 2 unit


Here, OMPN is rectangle.
P(22t,22t)

Mid point of MN=OP
(h,k)=(2t,2t)
Thus h×k=2t2t=2
Thus locus is the rectangular hyperbola xy=2
The director circle to this rectangular hyperbola is the point circle with center (0,0).
Thus distance between (0,0) and (1,1) is 2 unit

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