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Locus of Tangent Intersection on Curve

2175ExpertCalculusCoordinate Geometry

China Mathematical Competition

Suppose line $l$ through point $(0, 1)$ and curve $C: y = x + \frac{1}{x}$ ($x > 0$) intersect at two distinct points $M$ and $N$. Find the locus of the intersection points of the two tangent lines to curve $C$ at $M$ and $N$ respectively.
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