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a and b of a hyperbola from its eccentricity and an axis or latus rectum

This type of question, asked 2 times: 29 Jun 2022, 23 Jan 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    29 Jun 2022

    88
    Let H:x2a2−y2b2=1,a>0,b>0H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1,a > 0,b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(22+14)4(2\sqrt{2}+\sqrt{14}). If the eccentricity HH is 112\frac{\sqrt{11}}{2}, then value of a2+b2a^{2}+b^{2} is equal to

  2. Question 2

    23 Jan 2026 S1

    51
    Let the domain of the function f(x)=log⁡3log⁡5log⁡7(9x−x2−13)f(x) =\log_{3}\log_{5}\log_{7}\left( 9x -x^{2}- 13 \right) be the interval (m,n)(m,n). Let the hyperbola x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 have eccentricity n3\frac{n}{3} and the length of the latus rectum 8m3\frac{8m}{3}. Then b2−a2b^{2}-a^{2} is equal to :

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