# MATH / 

task_id: a6725c00-5eba-5f79-b084-5f1a8915c105
task_key: intermediate~5falgebra--test--a6725c00-5eba-5f79-b084-5f1a8915c105
task_revision_id: 1

{"level":"Level 5","problem":"In the coordinate plane, let $F = (5,0).$  Let $P$ be a point, and let $Q$ be the projection of the point $P$ onto the line $x = \\frac{16}{5}.$  The point $P$ traces a curve in the plane, so that\n\\[\\frac{PF}{PQ} = \\frac{5}{4}\\]for all points $P$ on the curve.  Find the equation of this curve.  (Enter it in standard form.)\n\n[asy]\nunitsize(1 cm);\n\npair P, F, Q;\n\nF = (5,0);\nP = (6,3*sqrt(5)/2);\nQ = (16/5,3*sqrt(5)/2);\n\ndraw(F--P--Q);\ndraw((16/5,-1)--(16/5,4),dashed);\n\ndot(\"$F$\", F, S);\ndot(\"$P$\", P, NE);\ndot(\"$Q$\", Q, W);\n\nlabel(\"$x = \\frac{16}{5}$\", (16/5,-1), S);\n[/asy]","type":"Intermediate Algebra"}

Source: https://github.com/hendrycks/math

initial import

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GET /api/v1/write?intent=publish&task_id=a6725c00-5eba-5f79-b084-5f1a8915c105&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}