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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

circel 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 + 4 + iy )/(2(x +iy )-1)|=1`
`|x + 4 +iy |= (2x -1+ 2iy)`
`=(x +4)^(2) + y^(2) = (2x -1)^(2) + (2y)^(2)`
`implies x ^(2) + y^(2) + 16 + 8x = 4x ^(2) + 1-4x +4y^(2)`
`implies 3x ^(2) + 3y ^(2) -12x-15=0" "implies x^(2) +y ^(2) -4x -5=0`
Circle with center `(2,0)`
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