{"status": "success", "data": {"description_md": "The parabola $P$ has focus $(0,0)$ and goes through the points $(4,3)$ and $(-4,-3)$.  For how many points $(x,y)\\in P$ with integer coordinates is it true that $|4x+3y|\\leq 1000$?\n\n$\\textbf{(A) }38\\qquad<br>\\textbf{(B) }40\\qquad<br>\\textbf{(C) }42\\qquad<br>\\textbf{(D) }44\\qquad<br>\\textbf{(E) }46\\qquad$\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 parabola  <span class=\"katex--inline\">P</span>  has focus  <span class=\"katex--inline\">(0,0)</span>  and goes through the points  <span class=\"katex--inline\">(4,3)</span>  and  <span class=\"katex--inline\">(-4,-3)</span> .  For how many points  <span class=\"katex--inline\">(x,y)\\in P</span>  with integer coordinates is it true that  <span class=\"katex--inline\">|4x+3y|\\leq 1000</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }38\\qquad\\textbf{(B) }40\\qquad\\textbf{(C) }42\\qquad\\textbf{(D) }44\\qquad\\textbf{(E) }46\\qquad</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": 5, "problem_name": "2014 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/14_amc12A_p24"}}