Ellipse Latus Rectum and Eccentricity (Jee Mains)

Ellipse

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Ellipse Latus Rectum and Eccentricity

Let the length of the latus rectum of an ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ (a > b), be 30. If its eccentricity is the maximum value of the function f(t) = $- \frac{3}{4}$ + 2t – t², then (a² + b²) is equal to -

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