{"status": "success", "data": {"description_md": "Let $a, b, x,$ and $y$ be real numbers with $a>4$ and $b>1$ such that $$\\frac{x^2}{a^2}+\\frac{y^2}{a^2-16}=\\frac{(x-20)^2}{b^2-1}+\\frac{(y-11)^2}{b^2}=1. $$Find the least possible value of $a+b.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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\">a, b, x,</span> and <span class=\"katex--inline\">y</span> be real numbers with <span class=\"katex--inline\">a&gt;4</span> and <span class=\"katex--inline\">b&gt;1</span> such that <span class=\"katex--display\">\\frac{x^2}{a^2}+\\frac{y^2}{a^2-16}=\\frac{(x-20)^2}{b^2-1}+\\frac{(y-11)^2}{b^2}=1.</span>Find the least possible value of <span class=\"katex--inline\">a+b.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 5, "problem_name": "2022 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_II_p13", "prev": "/problem/22_aime_II_p11"}}