MathDB
line segment of length greater than 10^6 between y = x^2 and y = x^2 - 1

Source: Tournament of Towns, Senior A-Level Paper, Spring 2020 , p1

June 3, 2020
parabolaSegmentanalytic geometryalgebra

Problem Statement

Consider two parabolas y=x2y = x^2 and y=x2āˆ’1y = x^2 - 1. Let UU be the set of points between the parabolas (including the points on the parabolas themselves). Does UU contain a line segment of length greater than 10610^6 ?
Alexey Tolpygo
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