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 the equation of L is

Options

A. `sqrt3 x + y + 2 - 3sqrt3 = 0`
B. `y - sqrt3 x + 2 + 3sqrt3 = 0`
C. `sqrt3 y - x + 3 + 2sqrt3 = 0`
D. `sqrt3 y + x - 3 +2sqrt3 = 0`

Explanation

The equations of lines passing through (3,-2) and inclined at `60^(@)` to the line `sqrt3 + y = 1` are given by
`y + 2 = (-3 pm tan 60^(@))/(1 pm (-sqrt3) tan 60^(@)) (x - 3)`
[Using : `y - y_(1) = (m pm tan 60^(@))/(1 pm m tan alpha ) ( x - x_(1))`]
`implies y + 2 = (-sqrt3 pm sqrt3)/(1 pm 3) (x - 3)`
`implies y + 2 = 0` and `y + 2 = sqrt3 (x - 3)`
`implies y + 2 = 0` and `y - sqrt3 x + 2 + 3 sqrt3 = 0`
Clearly `y - sqrt3 x + 2 + 3sqrt3 = 0` is the required line as it is not parallel to x-axis .