Question

Which of the following value(s) of $k$, the equation $\left|\frac{3z-1-i}{z+2+i}\right|=k$ represents a circle?

• A. $3$
• B. $2$
• C. $5$
• D. $\pi$

Answer 1

Answer: (B), (C), (D)

$5$
$\pi$
$2$

$|\frac{3-(1+i)}{z+2i}|=k$
$|\frac{z-\frac{1+i}{3}}{z+2i}|=\frac{k}{3}$
$\to$ $|\frac{z-z_1}{z-z_2}|=\frac{k}{3}$
The above expression represents a circle If
$\frac{k}{3}\ne 1$
$k\ne 3$
Hence $K>0$ and $K$ is not equal to $3$.
Hence
$KϵR^{+}-\left\{3\right\}$