{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"939efc4a-77dd-5744-9152-ea0a53018fe8","task_key":"intermediate~5falgebra--test--939efc4a-77dd-5744-9152-ea0a53018fe8","task_revision_id":"1","upstream_id":"","short_description":"In the coordinate plane, let $F = (4,0).$ Let $P$ be a point, and let $Q$ be the…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the coordinate plane, let $F = (4,0).$  Let $P$ be a point, and let $Q$ be the projection of the point $P$ onto the line $x = \\\\frac{25}{4}.$  The point $P$ traces a curve in the plane, so that\\n\\\\[\\\\frac{PF}{PQ} = \\\\frac{4}{5}\\\\]for all points $P$ on the curve.  Find the area of the region formed by the curve.\\n\\n[asy]\\nunitsize(1 cm);\\n\\npair P, F, Q;\\n\\nF = (4,0);\\nP = (5*Cos(60),3*Sin(60));\\nQ = (25/4,3*Sin(60));\\n\\ndraw(F--P--Q);\\ndraw((25/4,-1)--(25/4,3),dashed);\\n\\ndot(\\\"$F$\\\", F, S);\\ndot(\\\"$P$\\\", P, W);\\ndot(\\\"$Q$\\\", Q, E);\\n\\nlabel(\\\"$x = \\\\frac{25}{4}$\\\", (25/4,-1), S);\\n[/asy]\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}