Function Domain and Hyperbola Properties (Jee M…

Hyperbola

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Function Domain and Hyperbola Properties

Let the domain of the function f(x) = log₃log₅log₇ (9x – x² – 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 b² – a² is equal to :

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