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Geometry
2D Coordinate Geometry
Excel in math and science
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Given \(A=(5,0)\) and \(B=(0,4)\), what is the equation of the locus of points \(P\) such that \[ \lvert \overline{PA} \rvert^2- \lvert \overline{PB} \rvert^2=9?\]
Excel in math and science
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It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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by Brilliant Staff
Given \(A=(9,-1)\) and \(B=(-9,5)\), what is the equation of the locus of points \(P\) such that \[ \lvert \overline{AP} \rvert: \lvert \overline{BP} \rvert=1:2 ,\] where \(\lvert \overline{AP} \rvert\) denotes the length of \(\overline{AP}?\)
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
Let \(A=(6,-5)\) and \(B=(-6,1)\) be two vertices of triangle \( ABC.\) What is the locus of vertex \(C \) such that the centroid of \(\triangle ABC\) moves along the line \(2x+5y=1?\)
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
Let \(A=(-6,0)\), \(B=(3,-3)\) and \(C=(5,3)\). What is the equation of the locus of points \(P\) such that \[\lvert \overline{AP} \rvert^2+\lvert \overline{BP} \rvert^2=2 \lvert \overline{CP} \rvert^2?\]
Excel in math and science
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Our wiki is made for math and science
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If \(A=(-3,0)\) and \(B=(12,0),\) what is the equation for the locus of points \(P\) such that \(\lvert \overline{PA} \rvert =\lvert \overline{PB} \rvert,\) where \(\lvert \overline{PA} \rvert\) denotes the length of \( \overline{PA}?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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by Brilliant Staff