If  k=aba+b then the line  xa+yb=1 passes through the fixed point, then that point is

Substitute ab=k(a+b) in the equation xa+yb=1It implies that bx+ay=abbx+ay=ka+bbx−k+ay−k=0 The equation b(x−k)+a(y−k)=0 is in the form of λ1L1+λ2L2=0, which represents the  set of lines passing through the point of intersection of lines L1≡x−k=0 and L2≡y−k=0 The point of intersection of lines is (k,k) Therefore, the fixed point is (k,k)