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The value of a for the ellipse (x^2)/(a^...

The value of `a` for the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,(a > b),` if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola `x^2=2(y-2)` is ___

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