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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Introduction to Three Dimensional Geometry

  • question_answer
    The co-ordinates of the points A and B are (2, 3, 4) and (-2, 5, -4) respectively. If a point P moves so that \[P{{A}^{2}}-P{{B}^{2}}=k\] where k is a constant, then the locus of P is

    A) \[-8x+4y-16z+16=k\]

    B) \[-8x-4y-16z-16=k\]

    C) \[-8x+4y-16z-16=k\]

    D) None of these

    Correct Answer: C

    Solution :

    [c] \[\because \,\,\,\,P{{A}^{2}}-P{{B}^{2}}=k\] \[\therefore \,\,\,\,\,[{{(x-2)}^{2}}+{{(y-3)}^{2}}+{{(z-4)}^{2}}]\]             \[=[{{(x+2)}^{2}}+{{(y-5)}^{2}}+{{(z+4)}^{2}}]=k\] or  \[-8x+4y-16z-16=k,\]


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