# Intersecting lines

Geometry Level 3

If $$(a,b)$$ is a point of intersection of the lines $$x\cos\theta+y\sin\theta=3$$ and $$x\sin\theta -y\cos\theta=4$$, where $$\theta$$ is a parameter, then find the maximum value of $$2^W$$ where $$W = {\left( \dfrac{a+b}{\sqrt{2}} \right) }$$.

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