The axis of a parabola is along the line \( y=x \) and the distance...

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The axis of a parabola is along the line \( y=x \) and the distance of its vertex from origin is \( \sqrt{2} \) and that from its focus is \( 2 \sqrt{2} \). If vertex and focus both lie in the first quadrant, then the equation of the parabola is
(a) \( (x+y)^{2}=(x-y-2) \)
(b) \( (x-y)^{2}=(x+y-2) \)
(c) \( (x-y)^{2}=4(x+y-2) \)
(d) \( (x-y)^{2}=8(x+y-2) \)
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