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

$y = 0$

This describes 2 lines $\Rightarrow C$

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2006 AMC 12A Problems/Problem 11

Problem

Solution

See also