2006 AMC 12A 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}\qquad\mathrm{(B)}\ \text{one point}\qquad\mathrm{(C)}\ \text{two lines}\qquad\mathrm{(D)}\ \text{a circle}\qquad\mathrm{(E)}\ \text{the entire plane}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.