Intersection points on circle, part 2

Geometry Level 5

The parabola \(f(x)=x^2\) intersects the graph of \( g(x) = x^4 + ax^3 -2x^2+ bx +1\) at four distinct points. These four points on a same circle of area 10. Given that \(b>0\), find the value of \(\lfloor{1000b}\rfloor\).


This problem is part of Curves... cut or touch?
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