OAB is formed by the lines x^2-4 x y+y^2=0 and the line A B . The equation of line A B is 2 x+3 y-1=0 . Then the equation of the median of the triangle drawn from the origin is

Step-by-step solution

Let D be the midpoint of line AB . array ll & A = (x₁, y₁ ) B = (x₂, y₂ ) & D ( x₁+x₂ 2 , y₁+y₂ 2 ) array Combined equation of side OA and OB is x^2-4 x y+y^2=0 and equation of line AB is 2 x+3 y-1=0 Points A, B satisfy x^2-4 x y+y^2=0 and aligned & 2 x+3 y-1=0 & x= 1-3 y 2 aligned Substituting above value in x^2-4 x y+y^2=0 aligned & ( 1-3 y 2 )^2-4 ( 1-3 y 2 ) y+y^2=0 & (1-3 y)^2-8 y(1-3 y)+4 y^2=0 & 1-6 y+9 y^2-8 y+24 y^2+4 y^2=0 & 37 y^2-14 y+1=0 & Sum of roots = - b a = 14 37 & y₁+y₂= 14 37 aligned y -coordina