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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

A
3 unit
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B
23 unit
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C
25 unit
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D
2 unit
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Solution

## The correct option is D √2 unit Here, OMPN is rectangle. P≡(2√2t,2√2t) Mid point of MN=OP ∴(h,k)=(√2t,√2t) Thus h×k=√2t⋅√2t=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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