Difference between revisions of "2006 AMC 10A Problems/Problem 11"
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<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) \ } 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> | ||
== Solution == | == Solution == | ||
| + | Expanding the left side, we have | ||
| + | |||
| + | <math>x^2+2xy+y^2=x^2+y^2\Longrightarrow 2xy=0\Longrightarrow xy=0</math> | ||
| + | |||
| + | There are two lines described in this graph, horizontal and vertical where x=0 and y=0. Thus, our answer is '''(C)''' | ||
== See Also == | == See Also == | ||
*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] | ||
Revision as of 20:28, 3 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)
