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. `y + sqrt3x + 2-3sqrt=0`
B. ` -sqrt3x+2+3sqrt3=0`
C. `sqrt3y-x + 3 +2sqrt3=0`
D. `sqrt3y+x-3+2sqrt3=0`

Answer

B

Explanation

A straight line passing through P and making an angle of ` prop = 60^(@) ` is given by
`(y-y_(1))/(x-x_(1)) = (m +- tan x)/(1-+m tan x)`

` Rightarrow y= -sqrt3x + 1 Rightarrow y= -sqrt3 x + 1 Rightarrow m =-sqrt3`
Also ` tan prop = sqrt3`
` Rightarrow (y+2)/(x-3) = (m+- tan prop)/( 1 -+ m tan prop)`
` (y+2)/(x-3) = (-sqrt3 + sqrt3)/( 1-(-sqrt3) (sqrt3))`
` or (y+2)/(x-3) = (-sqrt3 -sqrt3)/(1+(-sqrt3)(sqrt3)) Rightarrow (y+2)/(x-3) = (-2sqrt3)/(1-3) = sqrt3`
` Rightarrow y+2=0 `
y+2 =0
y + 2 =0
` or y + 2 = sqrt3 x - 3 sqrt3 `
Neglecting , y +2 =0 as it does not intersect X -axis .