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(B) Given that the length of the transverse axis is $2a = 6$,so $a = 3$.Given that the length of the latus rectum is $\frac{2b^2}{a} = \frac{8}{3}$.Su

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$4x^2 - 9y^2 = 36$

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(B) Given that the length of the transverse axis is $2a = 6$,so $a = 3$.Given that the length of the latus rectum is $\frac{2b^2}{a} = \frac{8}{3}$.Substituting $a = 3$ into the equation: $\frac{2b^2}{3} = \frac{8}{3} \implies 2b^2 = 8 \implies b^2 = 4$.The standard equation of a hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.Substituting $a^2 = 9$ and $b^2 = 4$,we get $\frac{x^2}{9} - \frac{y^2}{4} = 1$.Multiplying by $36$,we get $4x^2 - 9y^2 = 36$.

If the lengths of the transverse axis and the latus rectum of a hyperbola are $6$ and $\frac{8}{3}$ respectively,then the equation of the hyperbola is $ . . . . . . $

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