Find the radius of the circle in complex plane given by $|z - i| = 3|z +2i|$ where $z$ is a point on the circle. I tried to arrange the following into the standard equation of the circle i.e $|z - z'| = r$ where $r$ is the radius, $z'$ is the centre and $z$ is a point on the circle.
I rearranged the following equation to $|z - i| / |z + 2i| = 3$.
Now I substituted $z = x + iy$ and rationalised the left hand side. After rationalising I could not arrange it to look like the standard form. Please share your solution.
Thank you.

$|z - i| = 3|z +2i|$
$x^2+(y-1)^2=9(x^2+(y+2)^2)$
$x^2+y^2-2y+1=9x^2+9y^2+36y+36$
$8x^2+8y^2+38y+35=0$
$x^2+y^2+\frac{19}{4}y+\frac {35}{8}=0$
$x^2+(y+\frac{19}{8})^2=\frac{81}{64}$
Circle is centered at $(0;-\frac{19}{8})$ with radius $r=\frac{9}{8}$
