A Circle Fraction Minimum

★ 7/10Parametrization Circles Trigonometric Identities analytic geometry inequality

Problem

Real numbers $x, y$ satisfy

x^2 + y^2 - 10x - 10y + 45 = 0.

Find the minimum value of

\frac{2x^2 - xy - y}{x}.

Answer

Solution

Difficulty	7/10
Topics	Parametrization, Circles, Trigonometric Identities, analytic geometry, inequality

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