If 2 x^2-5 x y+2 y^2=0 represents two sides of a triangle whose centroid is (1,1) , then the equation of the third side is

Step-by-step solution

Given equation are 2 x^2-5 x y+2 y^2=0 (x-2 y)(2 x-y)=0 x=2 y & y=2 x Let A(a, 2 a) & B(2 b, b) and one point (0,0) so a+2 b+0 3 =1 a+2 b=3 ... (i) & 2 a+b+0 3 =1 2 a+b=3 ... (ii) on solving we get, a =1, ~b =1 So equation of line passing through A (1,2) & B (2,1) is aligned & y-2= 1-2 2-1 (x-1) & y-2=-x+1 x+y-3=0 aligned