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The radius of the circle |z-i| / |z+i| =3 is?? How to solve this??

The radius of the circle |z-i| / |z+i| =3 is?? How to solve this??

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1 Answers

Arun
25750 Points
5 years ago
Dear student
 
put z = x + iy
 
|x + i(y – 1)| = 3 |x + i(y + 1)|
 
on squaring
 
x^2 + (y – 1)^2 = 9 x^2 + 9 (y + 1)^2
 
8x^2 + 8y^2 + 20y + 8 = 0
 
x^2 + y^2 + 20/8 y + 1 = 0
 
radius = sqrt (g^2  +f^2 – c) = sqrt (100/64 – 1) = sqrt(36/64) = 6/8

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