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Question

The angle of rotation of the axes so that the equation $$\sqrt{3}\mathrm{x}-\mathrm{y}+5=0$$ may be reduced to the form $$\mathrm{Y}=\mathrm{k}$$, where $$\mathrm{k}$$ is a constant is 


A
π6
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B
π4
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C
π3
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D
π12
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Solution

The correct option is B $$\dfrac{\pi}{3}$$
Let axis be rotated through an angle $$\theta $$ then 
$$ x= x^{1} \cos \theta - y^{1} \sin\theta $$
$$ y = x^{1} \sin \theta + y^{1} \cos\theta $$
$$ \sqrt{3}\times x -y +5 = 0$$
$$ \sqrt{3} (x^{1} \cos \theta - y^{1} \sin\theta) - (x^{1} \sin \theta + y^{1} \cos\theta) +5 = 0$$
$$x^{1} (\sqrt{3} \cos \theta - \sin\theta ) = 0$$
$$ \Rightarrow \tan\theta  = \sqrt{3}$$
$$ \theta = 60^{\circ} = \dfrac{\pi }{3}$$

Mathematics

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