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MathNet 1997 — Part 01 Question 35

Math Olympiad Vault · MathNet 1997 — Part 01

Question 35

The parabolas $y = x^{2} + p x + q$ are considered, which intersect the coordinate axes at three different points, through which a circle is drawn. Show that all the circles drawn by varying $p$ and $q$ in $\mathbb{R}$ pass through a fixed point, which will be determined.