Let the length of a latus rectum of an ellipse (x²)/(a²) + (y²)/(b²) = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t² + t + 11/12, t R, then a² + b² is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q162

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

Let the length of a latus rectum of an ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

be 10. If its eccentricity is the minimum value of the function

f(t) = t^2 + t + \tfrac{11}{12}

t \in \mathbb{R}

, then

a^2 + b^2

is equal to: