Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2015MathematicsStraight LinesActual

A straight line L through the point ( 3 , - 2 ) is inclined at an angle of 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. B3 y - x + 3 + 2 3 = 0
  3. C3 y + x - 3 + 2 3 = 0
  4. Dy - 3 x + 2 + 3 3 = 0

Correct answer

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

Step-by-step solution

Let m be the slope of the line, then tan ⁡ 60 o = m + 3 1 - m 3 ⇒ 3 = m + 3 1 - 3   m ⇒ ± 3 = m + 3 1 - 3   m ∴ 3 - 3 m = m + 3 or - 3 + 3 m = m + 3 4 m = 0 or 2 m = 2 3 m = 0 or m = 3 Since L intersects X -axis we take m = 3 and get y = 3 x + c Since it passes through 3 , - 2 , therefore line will become   y - 3 x + 2 + 3 3 = 0

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 JEE Main PYQs