The locus represented by the complex equation|z−2−i|=|z|sin(π4−argz) is the part of

Let z+iy=r(cosθ+isinθ) , then the equation is|(x−2)+i(y−1)|=r(12cosθ−12sinθ)                                        =12(rcosθ−rsinθ) Or (x−2)2+(y−1)2=12(x−y) Which is the part of a parabola with focus (2,1) and directrix x−y=0