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 $W = {\left( \dfrac{a+b}{\sqrt{2}} \right) }$ .

Intersecting lines

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