What is greatest possible argument of complex number satisfying |z-4|=Re(z):A.π/4B.2π/3C.π/3D.None

A nice question
let z = x+iy
then expanding we get

Now plotting this will result in parabola and one can clearly see that the maximum argument will corrospond to tangent from orign to the parabola (Plot and see)
so y= mx
(1)
(2)
using (1) and (2) we get
m=1
which implies the maximum argument is the option A