Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202315 Apr 2023Morning ShiftMathematicsStraight LinesActual

Consider the triangles with vertices A 2 , 1 , B 0 , 0 and C t , 4 , t = 0 , 4 . If the maximum and the minimum perimeters of such triangles are obtained at t = α and t = β respectively, then 6 α + 21 β is equal to ___________.

Correct answer

0

Step-by-step solution

Given, The triangles with vertices A 2 ,   1 ,   B 0 ,   0 and C t ,   4 ,   t = 0 ,   4 , And the maximum and the minimum perimeters of such triangles are obtained at t = α and t = β respectively, Now to minimise C A + C B , in below diagram take image of B in y = 4 , We get, B ' = 0 ,   8 Now finding, equation of A B ' we get, y - 8 = - 7 2 x - 0 Now, putting y = 4 in above equation we get, - 4 = - 7 2 x ⇒ x = 8 7 ⇒ β = 8 7 Now, maximum perimet

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