# A Fairly Normal Asymmetry Problem

Calculus Level 4

Let $$P$$ be a point (other than the origin) lying on the parabola $$y = x^{2}$$. The normal line to the parabola at $$P$$ will intersect the parabola at another point $$Q$$. The minimum possible value for the area bounded by the line $$PQ$$ and the parabola is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

Clarification: The normal line is the line perpendicular to the tangent line at a given point on a curve and which passes through the given point.

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