2006 AMC 12A Problems/Problem 11

Problem

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

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

Solution

$(x+y)^2=x^2+y^2$

$x^2 + 2xy + y^2 = x^2 + y^2$

$2xy = 0$

Either $x = 0$ or $y = 0$ . The union of them is 2 lines $\Rightarrow C$ .

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Preceded by Problem 10	AMC 12A 2006	Followed by Problem 12

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2006 AMC 12A Problems/Problem 11

Problem

Solution

See also