{"status": "success", "data": {"description_md": "Define $a\\clubsuit b=a^2b-ab^2$. Which of the following describes the set of points $(x, y)$ for which $x\\clubsuit y=y\\clubsuit x$?\n\n$\\textbf{(A)}\\ \\text{a finite set of points}\\\\ \\qquad\\textbf{(B)}\\ \\text{one line}\\\\ \\qquad\\textbf{(C)}\\ \\text{two parallel lines}\\\\ \\qquad\\textbf{(D)}\\ \\text{two intersecting lines}\\\\ \\qquad\\textbf{(E)}\\ \\text{three lines}$", "description_html": "<p>Define  <span class=\"katex--inline\">a\\clubsuit b=a^2b-ab^2</span> . Which of the following describes the set of points  <span class=\"katex--inline\">(x, y)</span>  for which  <span class=\"katex--inline\">x\\clubsuit y=y\\clubsuit x</span> ?</p>\n<p> <span class=\"katex--inline\">\\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}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2013 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10B_p15", "prev": "/problem/13_amc10B_p13"}}