Let the domain of the function f(x)= log ₃ log ₅ log ₇(9x-x²-13) be the interval (m, n). Let the hyperbola (x²)/(a²)-(y²)/(b²)=1 have eccentricity n/3 and the length of the latus rectum 8m/3. Then b²-a² is equal to:

Coordinate Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 23 Jan, Morning shift · Q1

JEE Main 202623 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the domain of the function

f(x)=\log_3\log_5\log_7(9x-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{8m}{3}

. Then

b^2-a^2

is equal to :