A straight line L through the point (3,-2) is inclined at an angle `60^@` to the line `sqrt(3)x+y=1`. If L also intersects the x-axis then find the equation of L .

Options

A. `y+sqrt(3)x +2-3sqrt(3) = 0`
B. `y-sqrt(3)x +2+3sqrt(3) = 0`
C. `sqrt(3)y -x +3 +2sqrt(3) = 0`
D. `sqrt(3)y +x -3 +2sqrt(3) = 0`

Explanation

Let the slope of the required line be m. Then
`|(m+sqrt(3))/(1-sqrt(3)m)| = sqrt(3)`
`therefore m+sqrt(3) = +-(sqrt(3)-3m)`
`therefore m=0 " or " m =sqrt(3)`
Therefore, the equation is
`y+2 = sqrt(3)(x-3)(m ne 0 " as given that line cuts the x-axis")`
`"or " sqrt(3)x-y-(2+3sqrt(3)) = 0`