Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2016MathematicsStraight LinesActual

A straight line through origin O meets the lines 3 y = 10 - 4 x and 8 x + 6 y + 5 = 0 at points A and B respectively. Then, O divides the segment A B in the ratio

Options

  1. A2 : 3
  2. B1 : 2
  3. C4 : 1
  4. D3 : 4

Correct answer

C. 4 : 1

Step-by-step solution

Let A r 1 cos θ ,   r 1 sin θ A Lies on straight line 4 x + 3 y = 10 ⇒ 4 r 1 cos θ + 3 r 1 sin θ = 10 ⇒ r 1 4 cos θ + 3 sin θ = 10 ⇒ r 1 = 10 4 cos θ + 3 sin θ Let B - r 2 cos θ ,   - r 2 sin θ B lies on line 8 x + 6 y + 5 = 0 ⇒ 8 - r 2 cos θ + 6 - r 2 sin θ + 5 = 0 ⇒ r 2 8 cos θ + 6 sin θ - 5 = 0 ⇒ r 2 = 5 8 cos θ + 6 sin θ ∴ r 1 r 2 = 4 1

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