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Cyclic quad on a parabola!

Source: ISI Entrance 2015

May 10, 2015
coordinatesgeometryalgebraconicsparabola

Problem Statement

Let y=x2+ax+by = x^2 + ax + b be a parabola that cuts the coordinate axes at three distinct points. Show that the circle passing through these three points also passes through (0,1)(0,1).
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