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Q.
If $|z-1|+|z+3| \leq 8$, then the range of values of $|z-4|$ is
Complex Numbers and Quadratic Equations
Solution:
Given $|z-1|+|z+3| \leq 8$
$\therefore z$ 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 $9$ .
