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Q.

$Length of the latus rectum of the hyperbola x y = c^{2} is equal to$

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a

$\sqrt{2} c$

b

$2 c$

c

$2 \sqrt{2} c$

d

$4 c$

answer is C.

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Detailed Solution

$Length of latus rectum = \frac{2 b^{2}}{a}$

$\begin{array}{l} For x y = c^{2}, a = b and \frac{a^{2}}{2} = c^{2} \\ Required length = 2 \cdot \frac{a^{2}}{a} = 2 a = 2 \sqrt{2} c \end{array}$

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