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

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`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (JEE MAIN)|9 Videos

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

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 .

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

Show that the equations of the straight lines passing through the point (3,-2) and inclined at 60^0 to the line sqrt(3)x+y=1 a r e y+2=0a n dy-sqrt(3)x+2+3sqrt(3)=0.

Show that the equations of eth straight lines passing through the point (3,-2) and inclined at 60^0 to the line sqrt(3)x+y=1a r ey+2=0a n dy-sqrt(3)x+2+3sqrt(3)=0.

Find the equations t the straight lines passing through the point (2,3) and inclined at an angle of 45^0 to the line \ 3x+y-5=0.

The equation of two straight lines through (7,9) and making an angle of 60^@ with the line x-sqrt3y-2sqrt3 = 0 is

If the straight line drawn through the point P(sqrt3,2) and making an angle (pi)/(6) with the x-axis meets the line sqrt3x-4y+8=0 at Q, find the length of PQ.

A Straight line drawn through the point A(2,1) making an angle pi//4 with positive x-axis intersects another line x+2y+1=0 in the point Bdot Find length A B .

The point (2,1) is translated parallel to the line L: x-y=4 by 2sqrt(3) units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is

The point (2,1) is translated parallel to the line L: x-y=4 by 2sqrt(3) units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is