{"status": "success", "data": {"description_md": "Let $P$ be the parabola with equation $y=x^2$ and let $Q = (20, 14)$. There are real numbers $r$ and $s$ such that the line through $Q$ with slope $m$ does not intersect $P$ if and only if $r < m < s$. What is $r + s$?\n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 26\\qquad\\textbf{(C)}\\ 40\\qquad\\textbf{(D)}\\ 52\\qquad\\textbf{(E)}\\ 80$\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>Let  <span class=\"katex--inline\">P</span>  be the parabola with equation  <span class=\"katex--inline\">y=x^2</span>  and let  <span class=\"katex--inline\">Q = (20, 14)</span> . There are real numbers  <span class=\"katex--inline\">r</span>  and  <span class=\"katex--inline\">s</span>  such that the line through  <span class=\"katex--inline\">Q</span>  with slope  <span class=\"katex--inline\">m</span>  does not intersect  <span class=\"katex--inline\">P</span>  if and only if  <span class=\"katex--inline\">r &lt; m &lt; s</span> . What is  <span class=\"katex--inline\">r + s</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 26\\qquad\\textbf{(C)}\\ 40\\qquad\\textbf{(D)}\\ 52\\qquad\\textbf{(E)}\\ 80</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": "2014 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12B_p18", "prev": "/problem/14_amc12B_p16"}}