The length of the latus rectum of the hyperbo | vedclass

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(A) The given equation of the hyperbola is $25x^2 - 16y^2 = 400$.Dividing both sides by $400$,we get:$\frac{25x^2}{400} - \frac{16y^2}{400} = 1$$\frac

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$\frac{25}{2}$

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(A) The given equation of the hyperbola is $25x^2 - 16y^2 = 400$.Dividing both sides by $400$,we get:$\frac{25x^2}{400} - \frac{16y^2}{400} = 1$$\frac{x^2}{16} - \frac{y^2}{25} = 1$Comparing this with the standard equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,we have $a^2 = 16$ and $b^2 = 25$.Thus,$a = 4$ and $b = 5$.The length of the latus rectum is given by the formula $\frac{2b^2}{a}$.Length $= \frac{2 	imes 25}{4} = \frac{50}{4} = \frac{25}{2}$.

The length of the latus rectum of the hyperbola $25x^2 - 16y^2 = 400$ is -

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