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A straight lines L through the point ( ...

A straight lines L through the point ( 3, 2) is inclined at an angle `60^@` to the line `sqrt3x +y =1` . If L also intersects the x-axis, then the equation of L is

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`

Text Solution

Verified by Experts

The correct Answer is:
B

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`
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