Geometry

2D Coordinate Geometry

Locus of Points

         

Given A=(5,0)A=(5,0) and B=(0,4)B=(0,4), what is the equation of the locus of points PP such that PA2PB2=9? \lvert \overline{PA} \rvert^2- \lvert \overline{PB} \rvert^2=9?

Given A=(9,1)A=(9,-1) and B=(9,5)B=(-9,5), what is the equation of the locus of points PP such that AP:BP=1:2, \lvert \overline{AP} \rvert: \lvert \overline{BP} \rvert=1:2 , where AP\lvert \overline{AP} \rvert denotes the length of AP?\overline{AP}?

Let A=(6,5)A=(6,-5) and B=(6,1)B=(-6,1) be two vertices of triangle ABC. ABC. What is the locus of vertex CC such that the centroid of ABC\triangle ABC moves along the line 2x+5y=1?2x+5y=1?

Let A=(6,0)A=(-6,0), B=(3,3)B=(3,-3) and C=(5,3)C=(5,3). What is the equation of the locus of points PP such that AP2+BP2=2CP2?\lvert \overline{AP} \rvert^2+\lvert \overline{BP} \rvert^2=2 \lvert \overline{CP} \rvert^2?

If A=(3,0)A=(-3,0) and B=(12,0),B=(12,0), what is the equation for the locus of points PP such that PA=PB,\lvert \overline{PA} \rvert =\lvert \overline{PB} \rvert, where PA\lvert \overline{PA} \rvert denotes the length of PA? \overline{PA}?

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