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 directo

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

TestHub · Accepted Answer

OMPN is rectangle.\ P = ( Ct , t c ​ ) Mid point = ( 2 c t ​ , 2 t c ​ ) = ( x , y ) ∴ cy = 4 c 2 ​ ⇒ e = 2 ​

Mathematics - Hyperbola Question with Solution | TestHub

Options:

Doubts & Discussion