1. Given the complex number
$$
(x-2)+(y-2) \mathrm{i} \quad (x, y \in \mathbf{R})
$$

the modulus of which equals $x \cos 45^{\circ}+y \sin 45^{\circ}+11$. Then the locus of the moving point $P(x, y)$ is ( ).
(A) circle (B) ellipse (C) hyperbola (D) parabola
-、1.D.
From the given, we have
$$
\sqrt{(x-2)^{2}+(y-2)^{2}}=\frac{|x+y+\sqrt{2}|}{\sqrt{2}} \text {. }
$$

This indicates that the moving point $P(x, y)$ is equidistant from the fixed point $F(2,2)$ and the fixed line $x+y+\sqrt{2}=0$. According to the definition, the locus of the moving point $P(x, y)$ is a parabola.