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Question

If |z1|+|z+3|8,then range of |z4| is

A
(0,5)
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B
(7,0)
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C
(1,9)
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D
(5,0)
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Solution

The correct option is C (1,9)
Given:
|z+3|+|z1|8
z lies on and inner region of the ellipse |z+3|+|z1|=8
From the figure:
Equation of ellipse is SP+SP=2a where, S & S' are focii and 2a is major axis.

|z+3|+|z1|=8
Comparing above eq with SP+SP=2a we get,

2a=8
a=4

min|z4|=distance between point P(4,0) & point A(3,0)=d(PA)

min|z4|=d(PA)=1

max|z4|=distance between point P(4,0) & point B(5,0)=d(PB)

max|z4|=d(PB)=9
min|z4||z4|max|z4|

1|z4|9

|z4|[1,9]

Hence, option 'C' is correct.

161523_157173_ans.JPG

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