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y = ax^2, intersect circle ((0,0),1) besides (0, 0)

Source: 2002 Swedish Mathematical Competition p3

March 21, 2021
parabolasystem of equationsSystemparameteralgebraanalytic geometry

Problem Statement

CC is the circle center (0,1)(0,1), radius 11. PP is the parabola y=ax2y = ax^2. They meet at (0,0)(0, 0). For what values of aa do they meet at another point or points?
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