The length of the latus rectum of the hyperbola $16 x^{2} - 25 y^{2} + 400 = 0$ is

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$\frac{32}{5}$

$\frac{16}{5}$

$\frac{25}{4}$

$\frac{25}{2}$

answer is D.

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Detailed Solution

$16 x^{2} - 25 y^{2} + 400 = 0$

$\begin{array}{l} \Rightarrow \frac{y^{2}}{16} - \frac{x^{2}}{25} = 1 \Rightarrow a^{2} = 25, b^{2} = 16 \\ ∴ Latus rectum = \frac{2 a^{2}}{b} = \frac{50}{4} = \frac{25}{2} . \end{array}$

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