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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