Question

If $|z-1|+|z+3|\le 8$, then the range of values of $|z-4|$ is

• A. (0, 8)
• B. [0, 8]
• C. [1, 9]
• D. [5, 9]

Answer 1

Answer: (C)

Given $|z-1|+|z+3|\le 8$
$\therefore z$ lies inside or on the ellipse whose foci are $(1,0)$
and $(-3,0)$ and vertices are $(-5,0)$ and $(3,0)$.

Now, $|z-4|$ is distance of $z$ from $(4,0)$.
Minimum distance is $1$ and maximum is $9$ .