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|z – 1| + |z + 3 | ≤ 8, then the range of values of |z – 4| is

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[1, 9]

[5, 9]

(0, 8)

[0, 8]

answer is C.

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Detailed Solution

Given |z – 1| + |z + 3| ≤ 8

$∴$ z lies inside or on the ellipse whose foci are (1, 0) and (–3, 0). 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.

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