Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainMathematicsStraight Lines

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

Options

  1. Ay+ 3 x+2-3 3 =0
  2. By- 3 x+2+3 3 =0
  3. C3 y-x+3+2 3 =0
  4. D3 y+x-3+2 3 =0

Correct answer

B. y- 3 x+2+3 3 =0

Step-by-step solution

A straight line passing through P and making an angle of =60^ , is given by y-y₁ x-x₁ = ( ) where, 3 x+y=1 y=- 3 x+1 Then, =- 3 array ll & y+2 x-3 = 1 & y+2 x-3 = - 3 + 3 1-(- 3 )( 3 ) and & y+2 x-3 = - 3 - 3 1+(- 3 )( 3 ) array array ll & y+2=0 and & y+2 x-3 = -2 3 1-3 = 3 & y+2= 3 x-3 3 array Neglecting, y+2=0 as it does not intersect Y -axis.

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is ( , ) , then 9( + ) is equal 2026Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All Highly selective Backlog Qs for JEE Main PYQs