Let, $z\in C\text{, }$the set of complex numbers. Then the equation $2|z+3i|-|z-i|=0$ represents

 

We have $2|z+3i|-|z-i|=0$

$\Rightarrow 2|x+i(y+3\left)\right|=|x+i(y-1\left)\right|(:z=x+iy)$

$\begin{array}{l}\Rightarrow 2\sqrt{x^2+(y+3{)}^2}=\sqrt{x^2+(y-1{)}^2}\\ \Rightarrow 4\left(x^2+(y+3{)}^2\right)=x^2+(y-1{)}^2\\ \Rightarrow 3x^2=y^2-2y+1-4y^2-24y-36\\ \Rightarrow 3x^2+3y^2+26y+35=0\\ \Rightarrow x^2+y^2+\frac{26}{3}y+\frac{35}{3}=0\end{array}$

This is the equation of circle with radius.

$r=\sqrt{0^2+{\left(\frac{13}{3}\right)}^2-\frac{35}{3}}=\sqrt{\frac{64}{9}}=\frac{8}{3}$