Home
Class 12
MATHS
A straight line L through the point (3,-...

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

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


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`
Promotional Banner

Similar Questions

Explore conceptually related problems

A straight line 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 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 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 .

A straight line L passes through (3,-2) also inclined at an angle 60^@ to the line sqrt(3x)+y=1.If L also intersects the x-axis, then the equation of L is: (A) y+sqrt(3x)+2-3sqrt3=0 (B) y-sqrt(3x)+2+3sqrt3=0 (C) sqrt(3y)-x+3+2sqrt3=0 (D) sqrt(3y)+x-3+2sqrt3=0

A straight line through the point (3, -2) is inclined at an angle 60^(@) to the line sqrt3x+y=1 . If it intersects the X-axis, then its equation will be

Find the equation of straight lines through the point A(3,-2) and inclined at 60^(@) to the line sqrt(3)x+y=1 .

A straight line passing through origin and inclined at 60^(@) to the line sqrt(3)x=y=1 is

One of the equations of the lines passing through the point (3, -2) and inclined at 60^(@) to the line sqrt(3)x+y=1 is :