Q42 / 160 · WBJEE 2011 · Mathematics

The length of the latus rectum of the ellipse \(16 x^2+25 y^2=400\) is

A
\(5 / 16\) unit
Correct answer
B
\(32 / 5\) unit
C
\(16 / 5\) unit
D
\(5 / 32\) unit

Solution

Hints : Length of latus rectum \(=2 \frac{b^2}{a}=\frac{2 \times 16}{5}=\frac{32}{5}\) \(\begin{aligned} & 16 x^2+25 y^2=400 \\ & \frac{x^2}{25}+\frac{y^2}{16}=1 \\ & a^2=25 ; b^2=16 \end{aligned}\)

Hence, the correct answer is option: 'B'.

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