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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The co-ordinates of the points A and B are (2, 3, 4) (-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) A line

    B) A plane

    C) A sphere

    D) None of these

    Correct Answer: B

    Solution :

    • \[\because \] \[P{{A}^{2}}-P{{B}^{2}}=k\]                   
    • \[\therefore \]  \[[{{(x-2)}^{2}}+{{(y-3)}^{2}}+{{(z-4)}^{2}}]\]           
    • \[-[{{(x+2)}^{2}}+{{(y-5)}^{2}}+{{(z+4)}^{2}}]=k\] or \[-\,8x+4y-16z-16=k\], which is the equation of a plane.


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