JEE Advance - Mathematics (1998 - No. 37)

A curve $$C$$ has the property that if the tangent drawn at any point $$P$$ on $$C$$ meets the co-ordinate axes at $$A$$ and $$B$$, then $$P$$ is the mid-point of $$AB$$. The curve passes through the point $$(1, 1)$$. Determine the equation of the curve.