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Q.

If |z−1|+|z+3|≤8  then the minimum and maximum values of |z−4|  respectively is

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a

1, 9

b

10, 15

c

16, 22

d

13, 18

answer is A.

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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) and vertices are (-5,0) and (3,0).  Clearly the minimum and maximum values of|z−4|  are 1 and 9 respectively representing the distances PA and PA’.∴1 |≤|z−4|≤9Hence option (1)
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