Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20258 Apr 2025Evening ShiftMathematicsStraight LinesActual

A line passing through the point P ( a , ) makes an acute angle with the positive x -axis. Let this line be rotated about the point P through an angle 2 in the clock-wise direction. If in the new position, the slope of the line is 2- 3 and its distance from the origin is 1 2 , then the value of 3 a^2 ^2 -2 3 is

Options

  1. A4
  2. B6
  3. C5
  4. D8

Correct answer

A. 4

Step-by-step solution

aligned & m _ PR =2- 3 = 15^ & 2 =15^ =30^ aligned equation of PR : aligned & y= 15^ (x-a) & y=(2- 3 )(x-a) aligned distance from origin = 1 2 aligned & | 3 a-2 a 4+3-4 3 +1 |= 1 2 & |a|(2- 3 ) 2 (2- 3 ) = 1 2 & |a|= 2 2- 3 = 2 ( 2+ 3 ) & a^2=2(2+ 3 ) & 3 a^2 ^2 -2 3 & 3 (4+2 3 ) 1 3 -2 3 =4 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 JEE Main PYQs