Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Paragraph: Through point O a straight line L₁ is drawn to cut two given straight lines 3 x+4 y-5=0 and x+2 y-3=0 at the points L & M , where O is origin. On the basis of above information answer the following : Question: The equation of line L₁ if O L: O M is equal to 5: 3 is -

Options

  1. Ax+2 y=0
  2. B2 x-y=0
  3. Cx+y=0
  4. Dx-y=0

Correct answer

C. x+y=0

Step-by-step solution

Let equation of straight line through O is x = y =r Let OL = r ₁ and OM = r ₂ , then the coordinates of L and M are given by L ( r ₁ , r ₁ ) and m ( r ₂ , r ₂ ) . Let N(h, k) be the variable point such that O N=r₃ , then h=r₃ , k=r₃ , since L and M lie on 3 x+4 y-5=0 and x+2 y-3=0 so r₁(3 +4 )=5 and r₂( +2 )=3 r ₁ r ₃ = 5 3 ~h +4 k and r ₂ r ₃ = 3 ~h +2 k aligned & Now r₁ r₂ = 5 3 & 5 (3 +4 ) ( +2 ) 3 = 5 3 & +2 =3 +4 & 2 +2 =0 =-1 & equation of L₁ will be x+y=0 aligned

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 Most Important Selected Qs for JEE Advanced PYQs