If \( (x, y) \) lies on the ellipse \( x^{2}+2 y^{2}=2 \), then maximum value of \( x^{2}+y^{2}+...

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If \( (x, y) \) lies on the ellipse \( x^{2}+2 y^{2}=2 \), then maximum value of \( x^{2}+y^{2}+\sqrt{2} x y-1 \) is
(a) \( \frac{\sqrt{5}+1}{2} \)
(b) \( \frac{\sqrt{5}-1}{2} \)
(c) \( \frac{\sqrt{5}+1}{4} \)
(d) \( \frac{\sqrt{5}-1}{4} \)
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