Length of the latusrectum of the hyperbola $x y = c$ ,is equal to

2 c

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\sqrt{2} c

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2 \sqrt{2} c

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4 c

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Solution

The correct option is C $2 \sqrt{2} c$
if co-ordinate axis is rotated by $45^{0}$
Then new equation of hyperbola is $(\frac{X - Y}{\sqrt{2}}) (\frac{X + Y}{\sqrt{2}}) = c$
$\Rightarrow X^{2} - Y^{2} = 2 c$
Therefore, length of latus rectum is $2 \frac{b^{2}}{a} = \frac{4 c}{\sqrt{2 c}} = 2 \sqrt{2} c$

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