Find equation of the line through the point (0, 2) making an angle `(2pi)/3`with the positive xaxis. Also, find the equation of line parallel to it and crossing the `x` -axis at a distance of `2` units below the origin.

Explanation

Slope of line, `m=tan"(2pi)/(3)=tan120^(@)`
`implies m=tan(180^(@)-60^(@))=-tan60^(@)=-sqrt(3)`
Equation of a line passing through the point `(0,2)`
and of slope `-sqrt(3)` is
`y-2=-sqrt(3)(x-0)`
`implies sqrt(3)+y-2=0`
Let equation of parallel line be `sqrt(3)x+y=lambda`.
This line intersects `y`-axis at `2` units below the origin i.e, line passes through the point `(0,-2)`
`:. 0-2=lambda`
`implies lambda=-2`
Therfore, equation of line is `sqrt(3)+y=-2`
`implies sqrt(3)x+y+2=0`