AMC 12 2006a Problem 11

Which of the following describes the graph of the equation $(x+y)^2=x^2+y^2$?

$\mathrm{(A)}\ \text{the empty set} \mathrm{(B)}\ \text{one point} \mathrm{(C)}\ \text{two lines} \mathrm{(D)}\ \text{a circle} \mathrm{(E)}\ \text{the entire plane}$