Length of latus rectum of hyperbola 25x^2 -16y^2 = 400 is -

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10-2. Parabola, Ellipse, Hyperbola

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

A

$\frac{25}{2}$

B

$\frac{16}{5}$

C

$\frac{15}{4}$

D

$\frac{4}{5}$

Solution

$\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$

$a^{2}=16, b^{2}=25$

length of latus rectum $=\frac{2 b^{2}}{a}=\frac{2 \times 25}{4}=\frac{25}{2}$

Standard 11

Mathematics

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