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Graph of equation

Source: AMC 12 2006A, Problem 11

February 5, 2006
AMC

Problem Statement

Which of the following describes the graph of the equation (x \plus{} y)^2 \equal{} x^2 \plus{} y^2?
<spanclass=′latex−bold′>(A)</span> the empty set<spanclass=′latex−bold′>(B)</span> one point<spanclass=′latex−bold′>(C)</span> two lines <span class='latex-bold'>(A)</span>\text{ the empty set}\qquad <span class='latex-bold'>(B)</span>\text{ one point}\qquad <span class='latex-bold'>(C)</span>\text{ two lines}
<spanclass=′latex−bold′>(D)</span> a circle<spanclass=′latex−bold′>(E)</span> the entire plane<span class='latex-bold'>(D)</span>\text{ a circle}\qquad <span class='latex-bold'>(E)</span>\text{ the entire plane}
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