Question

# A line cuts the y-axis at a distance of $$3$$ units from the origin and makes an angle of $${30}^{o}$$ with the positive direction of the x-axis. The equation of the line is

A
y3x+33=0
B
x3y+33=0
C
x+3y33=0
D
none of these

Solution

## The correct option is B $$x-\sqrt{3}y+3\sqrt{3}=0$$Here, $$m=\tan { { 30 }^{ o } } =\cfrac { 1 }{ \sqrt { 3 } } ;c=3\quad$$the eqution of the line is $$y=mx+c$$$$\quad y=\cfrac { 1 }{ \sqrt { 3 } } x+3\quad$$or $$\sqrt { 3 } y=x+3\sqrt { 3 } \Rightarrow x-\sqrt { 3 } y+3\sqrt { 3 } =0$$Mathematics

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