Let x^2/a^2+y^2/b^2=1(agtb) be a given ...

Let `x^2/a^2+y^2/b^2=1(agtb)` be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, `pphi(t)=5/2+t-t^2`, then `a^2+b^2` is equal to :

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