Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

A variable line through the point 6 5 , 6 5 cuts the coordinate axes at the points A and B respectively. If the point P divides A B internally in the ratio 2 : 1 , then the equation of the locus of P is

Options

  1. A5 x y = 2 x + y
  2. B5 x y = 2 2 x + y
  3. C5 x y = x + 2 y
  4. D5 x y = 2 x + 2 y

Correct answer

B. 5 x y = 2 2 x + y

Step-by-step solution

Let, A = a , 0 and B = 0 , b , then the equation of A B is x a + y b = 1 which passes through 6 5 , 6 5 ⇒ 1 a + 1 b = 5 6 Let, P = h , k , then h = 2 0 + 1 a 3 = a 3 & k = 2 b + 1 0 3 = 2 b 3 ⇒ a = 3 h & b = 3 k 2 ⇒ 1 3 h + 2 3 k = 5 6 ⇒ locus of P is 2 y + 2 x = 5 x y

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 NTA Abhyas JEE Main PYQs