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
B
π4
C
π3
D
π12

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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