Some parabolas of the form y=x
2+bx+c have three distinct intercepts (two x and one y). If for all such parabolas a circle is drawn through these three points, they will have a point in common.
Prove this assertion and find the point.
(In reply to
Solution by Brian Smith)
It seems you showed the vertex of the parabola is always inside the circle. An interesting fact that could have been it's own problem.
What this problem asks for, however, is the single point on the plane that all these circles have in common.
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Posted by Jer
on 2023-08-02 11:43:53 |
re: Solution
