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)