Question

A line cuts off an intercept of $$4$$ units on negative direction of the y-axis and makes an angle of $${120}^{o}$$ with the positive direction of the x-axis. The equation of the line is

A
3xy4=0
B
3x+y4=0
C
3x+y+4=0
D
none of these

Solution

The correct option is B $$\sqrt{3}x+y+4=0$$Here, $$\quad m=\tan { { 120 }^{ o } } =\tan { \left( { 180 }^{ o }-{ 60 }^{ o } \right) } =-\tan { { 60 }^{ o } } =-\sqrt { 3 } ;c=-4\quad$$the required equation is $$y=-\sqrt { 3 } -4\Rightarrow \sqrt { 3 } x+y+4=0$$Mathematics

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