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
B
2 unit
C
23 unit
D
25 unit

Solution

The correct option is A √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

Suggest corrections

Similar questions
View More

People also searched for
View More