Solution:
SOLUTION
Let z = x + iy = r ( cos θ + i sin θ ) then the equation is
$$\left| \left( x-2 \right)+i\left( y-1 \right) \right|=r\left( \cfrac{1}{\sqrt{2}}\cos \theta -\cfrac{1}{\sqrt{2}}\sin \theta \right)$$
$$=\cfrac{1}{\sqrt{2}}(r\cos \theta -r\sin \theta )$$
$$\sqrt{{{\left( x-2 \right)}^{2}}+{{\left( y-1 \right)}^{2}}}=\cfrac{1}{\sqrt{2}}\left( x-y \right)$$
Which is the part a parabola with focus (2, 1) and directrix x - y = 0
The correct answer is: parabola
