Circle Inscribed in a Parabola

Geometry Level 4

The area of a circle centered at the origin, which is inscribed in the parabola \(y=x^2-100,\) can be expressed as \( \frac{a}{b} \pi,\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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