{"status": "success", "data": {"description_md": "The parabolas $y=ax^2 - 2$ and $y=4 - bx^2$ intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area $12$. What is $a+b$?\n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 1.5\\qquad\\textbf{(C)}\\ 2\\qquad\\textbf{(D)}\\ 2.5\\qquad\\textbf{(E)}\\ 3$\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>The parabolas  <span class=\"katex--inline\">y=ax^2 - 2</span>  and  <span class=\"katex--inline\">y=4 - bx^2</span>  intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area  <span class=\"katex--inline\">12</span> . What is  <span class=\"katex--inline\">a+b</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 1.5\\qquad\\textbf{(C)}\\ 2\\qquad\\textbf{(D)}\\ 2.5\\qquad\\textbf{(E)}\\ 3</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": "2015 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p13", "prev": "/problem/15_amc12A_p11"}}