Let the domain of the function f(x)=\log _3 \log _5 \log _7 (9 x-x^2-13) be the interval ( m , n ). Let the hyperbola \frac{x^2}{ a ^2}-\frac{y^2}{b^2}=1 have eccentricity \frac{ n }{3} and the length of the latus rectum \frac{8 m}{3}. Then b ^2- a ^2 is equal to : [23 Jan 2026 Shift 1]

Hyperbola

Section: Mathematics

Question : 4 of 92

Marks: +1, -0

Let the domain of the function f(x)=log3log5log7(9x−x2−13) be the interval (m,n). Let the hyperbola ‌

−‌

=1 have eccentricity ‌

and the length of the latus rectum ‌

. Then b2−a2 is equal to :

[23 Jan 2026 Shift 1]

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