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If |(z +4)/(2z -1)|=1, where z =x +iy. ...

If` |(z +4)/(2z -1)|=1,` where `z =x +iy.` Then the point (x,y) lies on a:

A

circle with center (4,0)

B

circle with center (-2,0)

C

circle with center (2,0)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put z=x+iy
`|(x+u+iy)/(2(x-iy)-1)|=1`
|x+4+iy|=(2x-1+2iy)
`rArr (x+4)^2 + y^2=(2x-1)^2 +(2y)^2`
`rArr x^2+y^2+16+8x=4x^2+1-4x+4y^2`
`rArr 3x^2+3y^2-12x-15=0`
`rArr x^2+y^2-4x-5=0`
Circle with center (2,0)
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