The correct option is D Eccentricity =√2
Given, xy=18⇒c=3√2
Foci: (√2c,√2c) and (−√2c,−√2c)
Foci:(6,6) and (−6,−6)
Focal length =4c Focal length =4×3√2 Focal length =12√2 Focal length =√288
Directrix: x+y=±√2c
⇒x+y=±√2×3√2
⇒x+y=±6
For a rectangular hyperbola
Eccentricity =√2