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?

1 Answer

y=1/\sqrt3 x\pm4

Explanation:

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