Expanding the left side, we have
$x^2+2xy+y^2=x^2+y^2\Longrightarrow 2xy=0\Longrightarrow xy=0\Longrightarrow x = 0 \textrm{ or } y = 0$
Thus there are two lines described in this graph, the horizontal line $y = 0$ and the vertical line $x=0$. Thus, our answer is $\boxed{\textbf{(C) }\textrm{two\,lines}}$.