If the lines k x+2 y-4=0 and 5 x-2 y-4=0 are conjugate with respect to the circle x^2+y^2-2 x-2 y+1=0 , then k is equal to

Step-by-step solution

The lines k x+2 y-4=0 and 5 x-2 y-4=0 are conjugate with respect to the circle x^2+y^2-2 x-2 y+1=0 Then, necessary condition aligned & r^2 (a₁ a₂+b₁ b₂ )= (a₁ g+b₁ f-c₁ ) & (a₂ g+b₂ f-c₂ ) aligned From the above equation, aligned & a₁=k, b₁=2 c₁=-4 & a₂=5, b₂=-2 c₂=-4 & g=-1, f=-1 c=1 & r^2=g^2+f^2- c =1+1-1=1 aligned Now, by using equation (i) aligned & 1(5 k-1)=(-k-2+1)(-5+2+4) & 5 k-4=-k+2 & 6 k=6 & k=1 aligned