Question

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

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

Answer 1

The correct option is C [1, 9]

$\therefore$ z lies inside or on the ellipse whose foci are $(1,0)$ and $(-3,0)$ and vertices are $(-5,0)$ and $(3,0)$

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