A Cleaning Ball in a Groove

★ 7/10Extrema Tangent Circle conic sections analytic geometry

Problem

The axial cross-section of an industrial groove is part of the hyperbola $y^2-x^2=1$ (with $y\in[1,10]$ ). A spherical cleaning ball is placed in the groove; it must be able to reach and clean the very bottom of the groove. Find the maximum radius of the ball.

Answer

Solution

Difficulty	7/10
Topics	Extrema, Tangent Circle, conic sections, analytic geometry

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