perplexus.info :: Just Math : Circle's convergence

Circle's convergence (Posted on 2023-07-31)

Some parabolas of the form y=x²+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.

No Solution Yet Submitted by Jer

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

re(2): Solution

Comment 3 of 3 |

(In reply to re: Solution by Jer)

Thanks, but now taking another look I think I have made an error about the claim that the vertex is always in the circle.

I'll have to take another crack at it sometime.

Posted by Brian Smith on 2023-08-02 13:48:58

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info