Consider all parabolas of the form y = x2 + 2px + q (p, q real) which intersect the x- and y-axes in three distinct points. For such a pair p, q let C(p,q) be the circle through the points of intersection of the parabola y = x2 +2px+q with the axes. Prove that all the circles C(p,q) have a point in common.
[IrMO 2000, Paper 1, Question 5]
This space is here to avoid seeing the answers before trying the problem!
If you enjoy using this website then please consider making a donation - every little helps :-)
You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.
Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..
You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.