JEE Advance - Mathematics (1995 - No. 2)

Let $$y=f(x)$$ be a curve passing through $$(1,1)$$ such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area $$2.$$ From the differential equation and determine all such possible curves.
x + y = 2
xy = 1, x, y > 0
x - y = 2
x/y = 1, x, y > 0
x = 1

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