{"status": "success", "data": {"description_md": "Points $A$ and $B$ are on the parabola $y=4x^2+7x-1$, and the origin is the midpoint of $AB$. What is the length of $AB$?\n\n$\\mathrm{(A)}\\ 2\\sqrt5<br>\\qquad<br>\\mathrm{(B)}\\ 5+\\frac{\\sqrt2}{2}<br>\\qquad<br>\\mathrm{(C)}\\ 5+\\sqrt2<br>\\qquad<br>\\mathrm{(D)}\\ 7<br>\\qquad<br>\\mathrm{(E)}\\ 5\\sqrt2$\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>Points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  are on the parabola  <span class=\"katex--inline\">y=4x^2+7x-1</span> , and the origin is the midpoint of  <span class=\"katex--inline\">AB</span> . What is the length of  <span class=\"katex--inline\">AB</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 2\\sqrt5\\qquad\\mathrm{(B)}\\ 5+\\frac{\\sqrt2}{2}\\qquad\\mathrm{(C)}\\ 5+\\sqrt2\\qquad\\mathrm{(D)}\\ 7\\qquad\\mathrm{(E)}\\ 5\\sqrt2</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": "2004 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p19", "prev": "/problem/04_amc12B_p17"}}