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A bit of algebra... Tangent to circle meets parabola

Source: Baltic Way 1999

December 23, 2010
conicsparabolaanalytic geometryslopequadraticsalgebra

Problem Statement

The point (a,b)(a,b) lies on the circle x2+y2=1x^2+y^2=1. The tangent to the circle at this point meets the parabola y=x2+1y=x^2+1 at exactly one point. Find all such points (a,b)(a,b).
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