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If $| z - 1 | + | z + 3 | \leq 8$ then the range of values of $| z - 4 | i s____$

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$[1, 9]$

$(0, 8)$

$[0, 8]$

$[5, 9]$

answer is C.

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Detailed Solution

$A A^{1} = 2 a = 8 \Rightarrow a = 4$

Let $p (z)$ be a point on ellipse and $Q = (4, 0)$
$∴ | z - 4 | = | P Q |$
Min of $P Q = 1$ , max of $P Q = 9$

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