What is the equation of the line making an angle of 30° with positive 𝑥 − 𝑎𝑥𝑖𝑠 and at a distance of 2(3)^1/2 from the origin?

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Answer 1 · 2018-07-28T03:44:15

#y=1/\sqrt3 x\pm4#

The slope #m# of the line making an angle #\theta=30^\circ# with the positive x-axis is given as

#m=\tan\theta#

#=\tan30^\circ#

#=1/\sqrt3#

Now, let the equation of line be:

#y=1/\sqrt3 x+c#

Now, the distance of above line from origin #(0, 0)# is given as

#\frac{|1/\sqrt3\cdot 0-1\cdot 0+c|}{\sqrt{(1/\sqrt3)^2+(-1)^2}}=2\sqrt3#

#\frac{|c|}{2/\sqrt3}=2\sqrt3#

#|c|=2\sqrt3\cdot 2/\sqrt3#

#|c|=4#

#c=\pm 4#

Setting the values of #c# in the equation of line, we get two equations of unknown line on either side of origin as follows

#y=1/\sqrt3 x\pm4#