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$A B$ is a variable chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. If $A B$ subtends a right angle at the origin $O$, then $\frac{1}{OA^2}+\frac{1}{OB^2}$ equals to
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$\frac{1}{a^2}+\frac{1}{b^2}$
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