# Locus Lo Kamar

Algebra Level 5

Consider a point $$\displaystyle P(x,y)$$, which moves on the $$\displaystyle xy$$ plane on the path $$\displaystyle y=|\alpha x-1|+|\alpha x-2|+\alpha x$$, where $$\displaystyle \alpha= \sin \theta$$, and $$\displaystyle \theta \in \Big[0,\dfrac{\pi}{2}\Big]$$, never letting it's abscissa exceed $$\displaystyle 2$$. Let $$\displaystyle A$$ be the area of the region $$\displaystyle R$$ consisting of all the points $$\displaystyle P$$ lying in the first quadrant of the plane when $$\displaystyle \theta$$ can take all its values $$\displaystyle \theta \in \Big[0,\dfrac{\pi}{2}\Big]$$, then find $$\displaystyle \dfrac{6}{A}$$.

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