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

  • question_answer
    The coordinates of the points A and B are (a, 0) and \[(-a,\,0)\] respectively. If a point P moves so that \[P{{A}^{2}}-P{{B}^{2}}=2{{k}^{2}}\], when k is constant, then the equation to the locus of the point P , is   

    A) \[2ax-{{k}^{2}}=0\]

    B) \[2ax+{{k}^{2}}=0\]

    C) \[2ay-{{k}^{2}}=0\]

    D) \[2ay+{{k}^{2}}=0\]

    Correct Answer: B

    Solution :

    Let the point be (x, y),  Then  \[{{(x-a)}^{2}}+{{y}^{2}}-{{(x+a)}^{2}}-{{y}^{2}}=2{{k}^{2}}\] \[\Rightarrow \,\,-\,4ax-2{{k}^{2}}=0\,\,\Rightarrow \,\,2ax+{{k}^{2}}=0\].


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