Home
Class 11
MATHS
Two line from the family of lines (1+2la...

Two line from the family of lines `(1+2lambda)x-(1+lambda)y+1=0` and the line x+y=5 form an equilateral triangle. The equation of the two lines can be

A

`y-2=(2+sqrt3)(x-1)`

B

`y-2=(2-sqrt3)(x-1)`

C

`y-2=(-sqrt2)(x-1)`

D

`y-1=(3-sqrt2)(x-1)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-III Problems on point of intersection of lines and concurrency of lines) (LEVEL- II Integer Type Questions)|1 Videos
  • STRAIGHT LINES

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-IV Problems on Angle between lines, Foot, Image, Orthocentre, Circumcentre, Incentre, Angle Bisector and Locus) (LEVEL-I Staight Objective Type Questions)|40 Videos
  • STRAIGHT LINES

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-III Problems on point of intersection of lines and concurrency of lines) (LEVEL- I Straight Objective Type Question)|22 Videos
  • REVISION EXERCISE

    AAKASH SERIES|Exercise PROPERTIES OF TRIANGLES|57 Videos
  • TANGENT AND NORMAL

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|48 Videos

Similar Questions

Explore conceptually related problems

Show that the lines (x+2a)^2-3y^2=0,x=a form an equilateral triangle.

Show that the straight lines represented by (x+2a)^(2)-3y^(2)=0 and x=a form an equilateral triangle .

Knowledge Check

  • Every line of the system (1+2lambda)x+(lambda-1)y+2(1+2lambda)=0, lambda being a parameter, passes through a fixed point A. The equation of the line passing through A and parallel to the line 3x-y = 0 is

    A
    `3x-y+5=0`
    B
    `-3x+y+5=0`
    C
    `3x-y+6=0`
    D
    `3x-y+8=0`
  • The triangle formed by the pair of line 3x^2+48xy+23y^2=0 and the line 3x-2y+4=0 is

    A
    Equilateral
    B
    Isosceles
    C
    Right angled
    D
    Scalane
  • The pair of lines 6x^(2)+7xy+lambday^(2)=0(lambda ne -6) forms a rightangled triangle with x+3y+4=0 then lambda=

    A
    3
    B
    `-3`
    C
    `1//3`
    D
    `-1//3`
  • Similar Questions

    Explore conceptually related problems

    Prove that the lines represented by the equations x^(2)-4xy+y^(2)=0 and x+y=3 form an equilateral triangle.

    Show that the lines form an equilateral triangle and find its area x^(2)-4xy+y^(2)=0, x+y-3=0

    Show that the lines x^(2)+16xy-11y^(2)=0 form an equilateral triangle with the line 2x+y+1=0 and find its area.

    Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 and x-y+1+lambda_(2)(2x-y-2)=0 . Equation of a straight line that belong to both families is

    The equation to the pair of lines through the origin and forming an equilateral triangle with the line 4x – 3y + 1 = 0 is