# MATH / 

task_id: 939efc4a-77dd-5744-9152-ea0a53018fe8
task_key: intermediate~5falgebra--test--939efc4a-77dd-5744-9152-ea0a53018fe8
task_revision_id: 1

{"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"}

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

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