Directrix will Drive you Delirious

Algebra Level 5

The parabola PP has equation y=x2.y=x^2. The parabola PP' is an image of PP that was rotated clockwise about the focus of PP a total of θ\theta degrees, where 0θ180.0 \le \theta \le 180^{\circ}. If PP' is tangent to the directrix of P,P, then the smallest possible xx value of all points on PP' can be represented as ab-\dfrac{\sqrt{a}}{b} for positive integers aa and b.b. Find a+b.a+b.

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