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 $\Rightarrow C$ .

2006 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

Page

Toolbox

Search

2006 AMC 12A Problems/Problem 11

Problem

Solution

See also