The separate equations of the asymptotes of rectangular hyperbola $x^{2} + 2 x y cot 2 α - y^{2} = a^{2}$ are :

x cot α - y = 0, x tan α + y = 0

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x cot α + y = 0, x tan α + y = 0

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x cot α + y = 0, x tan α - y = 0

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x cot α - y = 0, x tan α - y = 0

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Solution

The correct option is C $x cot α - y = 0, x tan α + y = 0$
Combined equation of asymptotes of given hyperbola is given by
$x^{2} + 2 x y cot 2 α - y^{2} = 0$
$\Rightarrow x = \frac{- 2 y c o t 2 α \pm \sqrt{4 y^{2} c o t^{2} 2 α + 4 y^{2}}}{2} = - \frac{y (1 \pm c o s 2 α)}{s i n 2 α}$
Hence separate equation are, $x cot α - y = 0, x tan α + y = 0$

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