The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a
The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a
Hyperbola
Circle
Straight line
Ellipse
Solution
It is given that,
$\left|\frac{z-i}{z-2 i}\right|=2$
Let $z=x+i y$, then
$\begin{aligned}
& |x+i(y-1)|=2|x+(y-2) i| \\
\Rightarrow \quad & x^{2}+(y-1)^{2}=4\left[x^{2}+(y-2)^{2}\right] \\
\Rightarrow & 3 x^{2}+3 y^{2}-14 y+16=0 \text { represent a circle, so }
\end{aligned}$
locus of $z$ is a circle.
Hence, option (b) is correct.