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Find the locus of the point (x, y) in the plane

Source: MTRP 2015 Class 11-Multiple Choice Question: Problem 14 :-

September 21, 2020

complex numberscoordinate geometryalgebra

Problem Statement

z=x+i y

where

x

and

y

are two real numbers. Find the locus of the point

(x, y)

in the plane, for which

\frac{z+i}{z-i}

is purely imaginary (that is, it is of the form

i b

where

b

is a real number). [Here,

i=\sqrt{-1}

[*] A straight line [*] A circle [*] A parabole [*] None of these