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  • If  <img alt="\mathrm{z=x+i y \text { satisfies }|z|-2=0 \text { and }|z-i|-|z+5 i|=0}," src="/latex-image/?%5Cmathrm%7Bz%3Dx&plus;i%20y%20%5Ctext%20%7B%20satisfies%20%7D%7Cz%7C-2%3D0

If  \mathrm{z=x+i y \text { satisfies }|z|-2=0 \text { and }|z-i|-|z+5 i|=0}, then

Option: 1

\mathrm{x+2 y-4=0}


Option: 2

\mathrm{x^{2}+y-4=0}


Option: 3

\mathrm{x+2 y+4=0}


Option: 4

\mathrm{x^{2}-y+3=0}


Answers (1)

best_answer

\mathrm{|z|=2\text { and } |z-i|=|z+5 i|}

First is circle with cetre at origi ad radius 2 uits

Second is perpendicular isector of lie segmet joining (0,1) and (0,-5)

\mathrm{\Rightarrow y= -2} lie

only point (0,-2) lies on both

It satisfies option 3

Hence correct option is 3 

Posted by

Sanket Gandhi

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