The joint equation of the bisectors of the angles between the line x=5 and y =3 is

Step-by-step solution

Lines x=5 and y=3 are rewritten as L₁: x-5=0 and L₂: y-3=0 . The angle bisectors of two lines A₁x + B₁y + C₁ = 0 and A₂x + B₂y + C₂ = 0 are given by A₁x+B₁y+C₁ A₁^2+B₁^2 = A₂x+B₂y+C₂ A₂^2+B₂^2 With A₁=1 , B₁=0 , C₁=-5 and A₂=0 , B₂=1 , C₂=-3 , the denominators are both 1, so the equation simplifies to x-5 = (y-3) . This yields two bisectors: x-y-2=0 and x+y-8=0 . Their product forms the joint equation (x-y-2)(x+y-8)=0 Expanding gives x^2 - y^2 - 10x + 6y + 16 = 0 , which matches option A. A