Two Curves and a Distance

★ 7/10Parametrization AM-GM analytic geometry

Problem

Consider the hyperbola $C_1:x^2-y^2=1$ and the curve

C_2:\frac xy+\frac yx=x^2-y^2.

1. Find the number of intersection points of $C_1$ and $C_2$ . 2. Find the minimum distance from the origin $O$ to a point of $C_2$ .

Answer

Solution

Difficulty	7/10
Topics	Parametrization, AM-GM, analytic geometry

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