perplexus.info :: Just Math : Parabola and Circle Dance

Parabola and Circle Dance (Posted on 2024-05-01)

Let y=x²+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).

No Solution Yet Submitted by Danish Ahmed Khan

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a graphical look (not a proof)

| Comment 1 of 2

Link to a Desmos graphic:

https://www.desmos.com/calculator/sxl1abhozd

Changing values for a and b, one can observe that the claim is true provided the parabola has at least one x-axis intercept.

Posted by Larry on 2024-05-01 09:39:03

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