Let \( a \) and \( b \) are positive number. If \( (x, y) \) is a point on the curve \( a x^...

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Let \( a \) and \( b \) are positive number. If \( (x, y) \) is a point on the curve \( a x^{2}+b y^{2}=a b \) then the largest possible value of \( x y \) is
(a) \( \frac{\sqrt{a b}}{2} \)
(b) \( \sqrt{a b} \)
(c) \( \frac{a b}{a+b} \)
(d) \( \frac{2 a b}{a+b} \)
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