Straight Lines

JEE Main 2025 (Online) 23rd January Evening ShiftMCQHard📈 Topic in 3% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0, respectively. If the locus of the point P, that divides the rod AB internally in the ratio 2:1 is 9 (x2+ y2+ xy+ x+28y )-76=0, then - - is equal to :

Answer

(4) 23

Solution

Let A(a,a+2), B(b,-2) and P(h,k) with AP:PB=2:1.

[figure]

h= a+2b3, k= a-23 a=3k+2, b= 3h-3k-22; put in AB2=(a-b)2+(a+4)2=64

9 [(3k-h+2)2+4(k+2)2 ]=256 9 (h2+13k2-6hk-4h+28k )-76=0

=13, =-6, =-4 - - =23

Answer: (4)

Keep practising — Straight Lines

Ques. 2JEE Main 2025, 22 January (Morning Shift)

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2y=2. If the centroid of is the point ( , ), then 15( - ) is equal to :

Ques. 3JEE Main 2025, 22 January (Evening Shift)

Let A(6,8), B(10 ,-10 ) and C(-10 ,10 ), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5a-3h+6k+100 2 ) is equal to .

Ques. 4JEE Main 2025, 22 January (Evening Shift)

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2 is equal to .

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