Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsStraight Lines

The lines 2 x+3 y=6,2 x+3 y=8 cut the X -axis at A and B , respectively. A line L drawn through the point (2,2) meets the X -axis as C in such a way that abscissae of A, B and C are in arithmetic progression. Then, the equation of the line L is

Options

  1. A2 x+3 y=10
  2. B8 x+2 y=10
  3. C2 x-3 y=10
  4. D8 x-2 y=10

Correct answer

A. 2 x+3 y=10

Step-by-step solution

Given lines are 2 x+3 y=6 and 2 x+3 y=8 These lines meet the X -axis at A(3,0) and B(4,0) . The line L passes through (2,2) cuts X -axis at C , such that x -coordinate of A, B, C are in ap i.e. 3,4, x₁ array ll & 2.4=3+x₁ & x₁=8-3=5 array To coordinates of C are (5,0) . A line L passing through the points (2,2) and (5,0) , is aligned & y-0 & = 0-2 5-2 (x-5) & y & = -2 3 (x-5) & 3 y & =-2 x+10 & 2 x+3 y & =10 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 99 Percentile Qs Bank for JEE Main PYQs