PYQ Vault
EbooksTutor

Ellipse with a given latus rectum whose eccentricity is the extreme value of a quadratic: find a^2 + b^2

The same question, asked 2 times: 7 Apr 2025*, 24 Jan 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    7 Apr 2025

    137
    Let the length of a latus rectum of an ellipse x2a2+y2b2=1\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)=t2+t+1112f(t) =t^{2}+t+\frac{11}{12}, t∈Rt \in R, then a2+b2a^{2}+b^{2} is equal to :

    Tap an option to check your answer.

  2. Question 2

    24 Jan 2026 S2

    52
    Let the length of the latus rectum of an ellipse x2a2+y2 b2=1,(a>b)\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,(a > b), be 30 . If its eccentricity is the maximum value of the function f(t)=−34+2t−t2f(t) = -\frac{3}{4}+ 2t -t^{2}, then (a2+b2)\left( a^{2}+b^{2} \right) is equal to -

    Tap an option to check your answer.