Question

The equation of the line passing through
(1, 2) and making an angle of 30° in clockwise direction with the positive direction of y-axis is .

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

Answer 1

The correct option is C $\sqrt{3}x-y+2-\sqrt{3}=0$

As the given line makes an angle of 30$°$ in clockwise direction with the positive direction of y-axis, hence it will make an angle of 60$°$ in anti-clockwise direction with the positive direction of x-axis.
$\mathrm{So},\mathrm{slope}\mathrm{of}\mathrm{the}\mathrm{line},m=\tan 60°=\sqrt{3}.\therefore \mathrm{Equation}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{passing}\mathrm{through}\left(1,2\right)\mathrm{and}\mathrm{having}\mathrm{slope}\sqrt{3}\mathrm{is}y-2=\sqrt{3}\left(x-1\right)\Rightarrow \sqrt{3}x-y+2-\sqrt{3}=0$