IIT JEE , AIEEE Forum - Mathematics , Algebra

twinkle_star

if # = z / z - (1/3 i)

and | # | = 1

then

z lies on????????

a) circle

b) ellipse

c) hyperbola

d)none of these

nadeemoidu

| z / (z - i/3 ) | =1

| z | = | z- i/3 |

|z| is the distance of z from the origin.
|z-i/3 | is the distance of z from the point ( 0 , 1/3) .

distance of z from 2 points are equal . the locus is a straight line

ritu_007

hiiiii

given I#I=1

#= z/z-(1/3i)

put z= x+iy

IzI/Iz-(1/3i)I=1

Ix+iyI/Ix+i(y-1/3)I=1

x²+y^{2 =}

x²+(y-1/3)²

x²+y²=x²+y²+1/9-2/3y

so it passes through y=0,which is a straight line.

so ans=(d).

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