If $\left|z-1\right|+\left|z+3\right|\le 8$  then the minimum and maximum values of $\left|z-4\right|$  respectively is

Given $\left|z-1\right|+\left|z+3\right|\le 8$

$\therefore$  $z$  lies inside or on the ellipse whose foci are (1, 0) and (-3, 0) and vertices are (-5,0) and (3,0).  Clearly the minimum and maximum values of$\left|z-4\right|$  are 1 and 9 respectively representing the distances PA and PA’.

$\therefore 1|\le |z-4|\le 9$

Hence option (1)