Question

Equation of line(s) passing through $(0,0)$ and making an angle of ${30}^{\text{o}}$ with the line $x-y+3=0$ is/are

• A. $y=(2-\sqrt{3})x$
• B. $y=\frac{1}{\sqrt{3}}x$
• C. $y=(2+\sqrt{3})x$
• D. $x-(\sqrt{3}-1)y=0$

Answer 1

Answer: (A), (C)

$y=(2+\sqrt{3})x$

Given line is $x-y+3=0$
$\Rightarrow m=1\Rightarrow \theta ={45}^{\text{o}}$

Required line makes ${30}^{\circ }$ with this line.
So, required line makes angle of ${15}^{\circ }$ or ${75}^{\circ }$ with the $x-$axis.

Required line equation is
$y=\tan \left({15}^{\circ }\right)x$
$\Rightarrow y=(2-\sqrt{3})x$ or
$y=\tan \left({75}^{\circ }\right)x$
$\Rightarrow y=(2+\sqrt{3})x$