Question

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

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{12}$

Answer 1

Answer: (C)

$\frac{\pi }{3}$

Let axis be rotated through an angle $\theta$ then

$x=x^1\cos \theta -y^1\sin \theta$

$y=x^1\sin \theta +y^1\cos \theta$

$\sqrt{3}\times x-y+5=0$

$\sqrt{3}(x^1\cos \theta -y^1\sin \theta )-(x^1\sin \theta +y^1\cos \theta )+5=0$

$x^1(\sqrt{3}\cos \theta -\sin \theta )=0$

$\Rightarrow \tan \theta =\sqrt{3}$

$\theta ={60}^{\circ }=\frac{\pi }{3}$