IrMO 2000 P1 Q5: Upper Secondary Mathematics Competition Question

Consider all parabolas of the form y = x² + 2px + q (p, q real) which intersect the x- and y-axes in three distinct points. For such a pair p, q let C(p,q) be the circle through the points of intersection of the parabola y = x² +2px+q with the axes. Prove that all the circles C(p,q) have a point in common.


[IrMO 2000, Paper 1, Question 5]

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