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2D Coordinate Geometry
In the 1600s, René Descartes married algebra and geometry to create the Cartesian plane.
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.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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
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.
Used and loved by 4 million people
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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
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.
Used and loved by 4 million people
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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
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.
Used and loved by 4 million people
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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
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.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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 \( \overline{PA}?\)