Easy to guess, somewhat hard to prove!

Algebra Level 2

If \(x^{2}\)+\(a^{2}\) = \(y^{2}\)+\(b^{2}\) = (\(a\times x\)) + (\(b\times y\)) = 1,

then the numerical value of \(a^{2}\) + \(b^{2}\) is

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