Difference between revisions of "2006 AMC 10A Problems/Problem 11"
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Which of the following describes the graph of the equation <math>\displaystyle(x+y)^2=x^2+y^2</math>? | Which of the following describes the graph of the equation <math>\displaystyle(x+y)^2=x^2+y^2</math>? | ||
| − | <math> \mathrm{(A) \ } the empty set\qquad \mathrm{(B) \ } one point\qquad \mathrm{(C) \ } two lines\qquad \mathrm{(D) \ } a circle\qquad \mathrm{(E) \ } the entire plane </math> | + | <math> \mathrm{(A) \ } \text{the empty set}\qquad \mathrm{(B) \ } one point\qquad \mathrm{(C) \ } two lines\qquad \mathrm{(D) \ } a circle\qquad \mathrm{(E) \ } the entire plane </math> |
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== Solution == | == Solution == | ||
Expanding the left side, we have | Expanding the left side, we have | ||
Revision as of 16:46, 15 July 2006
Problem
Which of the following describes the graph of the equation 
?
Solution
Expanding the left side, we have
There are two lines described in this graph, horizontal and vertical where x=0 and y=0. Thus, our answer is (C)
