The area of \({\bf 2 x^2 - xy + 2y^2 - 2 = 0 }\) can be represented as \( {\bf \large \frac{a \pi}{\sqrt{b}}, }\) where \({\bf a}\) and \({\bf b}\) are coprime positive integers and \({\bf b}\) is square free.

\(\)

Find: \({\bf a + b .}\)

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