{"status": "success", "data": {"description_md": "For how many integer values of $k$ do the graphs of $x^2+y^2=k^2$ and $xy = k$ not intersect?\n\n$\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 1 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ 4 \\qquad \\textbf{(E)}\\ 8$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For how many integer values of  <span class=\"katex--inline\">k</span>  do the graphs of  <span class=\"katex--inline\">x^2+y^2=k^2</span>  and  <span class=\"katex--inline\">xy = k</span>  not intersect?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 1 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ 4 \\qquad \\textbf{(E)}\\ 8</span> </p>&#10;<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": "2010 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p14", "prev": "/problem/10_amc12A_p12"}}