Equation of the rectangular hyperbola whose focus is (1,-1) and the corresponding directrix is x - y + 1 =  0 is

Eccentricity of rectangular hyperbola is 2∴ Equation of hyperbola is (x−1)2+(y+1)2=2|x−y+1|12+(−1)2or  (x−1)2+(y+1)2=(x−y+1)2or  2xy−4x+4y+1=0