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Parabola and Circle Dance (
Posted on 2024-05-01
)
Let y=x
2
+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).
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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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