Difference between revisions of "2013 AMC 10B Problems/Problem 14"

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==Problem==
 
Define <math> a\clubsuit b=a^2b-ab^2 </math>. Which of the following describes the set of points <math> (x, y) </math> for which <math> x\clubsuit y=y\clubsuit x </math>?
 
Define <math> a\clubsuit b=a^2b-ab^2 </math>. Which of the following describes the set of points <math> (x, y) </math> for which <math> x\clubsuit y=y\clubsuit x </math>?
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<math> \textbf{(A)}\ \text{a finite set of points}\ \qquad\textbf{(B)}\ \text{one line}\ \qquad\textbf{(C)}\ \text{two parallel lines}\ \qquad\textbf{(D}}\ \text{two intersecting lines}\ \qquad\textbf{(E)}\ \text{three lines} </math>

Revision as of 17:12, 21 February 2013

Problem

Define $a\clubsuit b=a^2b-ab^2$. Which of the following describes the set of points $(x, y)$ for which $x\clubsuit y=y\clubsuit x$?

$\textbf{(A)}\ \text{a finite set of points}\ \qquad\textbf{(B)}\ \text{one line}\ \qquad\textbf{(C)}\ \text{two parallel lines}\ \qquad\textbf{(D}}\ \text{two intersecting lines}\ \qquad\textbf{(E)}\ \text{three lines}$ (Error compiling LaTeX. Unknown error_msg)