Question

The complex numbers `z=x+iy` which satisfy the equation `|(z-5i)/(z+5i)|=1` lie on (a) The x-axis (b) The straight line `y=5` (c) A circle passing through the origin (d) Non of these
A. the X-axis
B. the straight line y=5
C. a cicle passing through the origin
D. None of these

Answer 1

Correct Answer - A
Given ,`|(z-5i)/(z+5i)| =1 rArr|z-5i|=|z+5i|`
`[because if |z-z_1|=|z-z_2|` then it is perpendicular bisector of `z_1 and z_2`]

`because` Perpendicular bisector (0,5) and (0,-5) is x- axis