Signed Areas on a Circle

★ 6/10Extrema Circles Completing the Square conic sections analytic geometry

Problem

Let $C$ be the curve $x^2 + y^2 = 2x - 4y$ . Points $P(x_1, y_1)$ , $Q(x_2, y_2)$ , $R(x_3, y_3)$ lie on $C$ . Find the minimum value of

x_1 y_2 - x_2 y_1 + x_2 y_3 - x_3 y_2.

Answer

Solution

Difficulty	6/10
Topics	Extrema, Circles, Completing the Square, conic sections, analytic geometry

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