MathDB
Parabolas producing Circumcircles with Common Point

Source: Spain 1997, #3

October 29, 2016
conicsparabolageometrycircumcircleTriangle

Problem Statement

For each parabola y=x2+px+qy = x^2+ px+q intersecting the coordinate axes in three distinct points, consider the circle passing through these points. Prove that all these circles pass through a single point, and find this point.