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2006 AMC 12A Problems/Problem 11

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The following problem is from both the 2006 AMC 12A #11 and 2008 AMC 10A #11, so both problems redirect to this page.

Problem

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)}\...

Solution

\begin{align*}(x+y)^2&=x^2+y^2\\x^2 + 2xy + y^2 &= x^2 + y^2\\2xy &= 0\end{align*} Either x = 0 or y = 0. The union of them is 2 lines, and thus the answer is \mathrm{(C)}.

draw((0,-50)--(0,50));draw((-50,0)--(50,0));

See also

2006 AMC 12A (Problems • 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
2006 AMC 10A (Problems • 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
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