{"status": "success", "data": {"description_md": "Let $C$ be the graph of $xy = 1$, and denote by $C^*$ the reflection of $C$ in the line $y = 2x$. Let the equation of $C^*$ be written in the form<br>\n$$ 12x^2 + bxy + cy^2 + d = 0. $$ Find the product $bc$.\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\">C</span> be the graph of <span class=\"katex--inline\">xy = 1</span>, and denote by <span class=\"katex--inline\">C^*</span> the reflection of <span class=\"katex--inline\">C</span> in the line <span class=\"katex--inline\">y = 2x</span>. Let the equation of <span class=\"katex--inline\">C^*</span> be written in the form<br/><span class=\"katex--display\"> 12x^2 + bxy + cy^2 + d = 0. </span><br/>Find the product <span class=\"katex--inline\">bc</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": 6, "problem_name": "1988 AIME Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/88_aime_p15", "prev": "/problem/88_aime_p13"}}