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