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BALTIC-WAY 1999 Problem 5

  • Answer

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).

Dataset text NuminaMath olympiads. Quoted with source.

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(-1,0),(1,0),(0,1),\left(-\frac{2 \sqrt{6}}{5},-\frac{1}{5}\right),\left(\frac{2 \sqrt{6}}{5},-\frac{1}{5}\right)

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