Equation of the rectangular hyperbola whose focus is P \( (1,-1) \)...

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

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(1) \( x^{2}-y^{2}=1 \)
(2) \( x y=1 \)
(3) \( 2 x y-4 x+4 y+1=0 \)
(4) \( 2 x y+4 x-4 y-1=0 \)
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