A Circle Through Three Intercepts

★ 7/10Circles conic sections analytic geometry Vieta's Formulas

Problem

The parabola $y = x^2 + bx + c$ meets the coordinate axes at three points $A, B, C$ . Prove that the circumcircle of $\triangle ABC$ always passes through a fixed point $P$ , independent of $b$ and $c$ .

Answer

Solution

Difficulty	7/10
Topics	Circles, conic sections, analytic geometry, Vieta's Formulas

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