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If |z-2-i|=|z|sin(pi/4-a r g z)| , wher...

If `|z-2-i|=|z|sin(pi/4-a r g z)|` , where `i=sqrt(-1)` ,then locus of z, is

A

a pair of straing lines

B

circle

C

parabola

D

ellispe

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`|(x-2)+i(y-1)|=|z||(1)/(sqrt2)costheta-(1)/(sqrt2)sintheta|`
where `theta =arg z`.
`sqrt((x-2)^(2)+(y-1)^(2))=(1)/(sqrt2)|x-y|`,
which represents a parabola
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