If principal argument of  $Z_0$  satisfying $\left|Z–3\right|\le \sqrt{2}$  and   $\arg \left(Z-5i\right)=-\frac{\pi }{4}$simultaneously is $\theta$ , then identify the correct statement(s)

 
arg(Z-5i) =  $\frac{-\pi }{4}$
(x + i (y-5)) =$\frac{-\pi }{4}$   
 y – 5 = –x
 x + y – 5 = 0
Also$\left|Z–3\right|\le \sqrt{2}$    
${\left(x-3\right)}^2+y^2\le 2$

Let Z₀ be the point of contact of line and Circle 
 Z₀ = 4 + i
$Tan\theta =\frac{1}{4}$,   $Tan2\theta =\frac{2\left(1/4\right)}{1-1/16}=\frac{8}{15}$
And  ,  $\left|Z_0\right|=\sqrt{17},\left|Z_0-5i\right|=4\sqrt{2}$