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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Transformation of axes and Locus

  • question_answer
    If P = (1,0), Q =(-1,0) and R =(2,0) are three given points, then the locus of a point S satisfying the relation \[S{{Q}^{2}}+S{{R}^{2}}=2S{{P}^{2}}\] is [IIT 1988]

    A) A straight line parallel to x-axis

    B) A circle through origin

    C) A circle with centre at the origin

    D) A straight line parallel to y-axis

    Correct Answer: D

    Solution :

    Let \[S\,(x,\,y),\] then  \[{{(x+1)}^{2}}+{{y}^{2}}+{{(x-2)}^{2}}+{{y}^{2}}=2\,[{{(x-1)}^{2}}+{{y}^{2}}]\] \[\Rightarrow \,\,2x+1+4-4x=-4x+2\,\,\Rightarrow \,\,x=-\frac{3}{2}\] Hence it is a straight line parallel to y-axis.


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