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Unit Circles and Parabolas

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This may seem completely random, but my roommate and I were having an argument about whether or not there is a set of parabolas that, when paired together, a circle tangent to both of them could be a unit circle. He's positive that it's possible, but I'm not convinced, knowing that parabolas increase at different rates at different times, and a unit circle, being a constant shape and having a constant diameter, could not effectively be placed in between them for infinity.


Any ideas?


(And if you need clarifications, just ask. It seems a bit confusing, and I'm not in the state of mind right now to fix it.. Sorry! :doh:)

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