JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer If \[(2,\,\,3,\,\,5)\] are ends of the diameter of a sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x\]\[-12y-2z+20=0\]. Then coordinates of the other end are

    A) \[(4,\,\,9,\,\,-3)\]                            

    B) \[(4,\,\,3,\,\,5)\]

    C) \[(4,\,\,3,\,\,-3)\]                            

    D) \[(4,\,\,-3,\,\,9)\]

    Correct Answer: A

    Solution :

     Let the co-ordinate of other ends are\[(x,\,\,y,\,\,z)\]. The centre of sphere is\[C(3,\,\,6,\,\,1)\]. Therefore,\[\frac{x+2}{2}=3\Rightarrow x=4\]           \[\frac{y+3}{2}=6\Rightarrow y=9\]and\[\frac{z+5}{2}=1\Rightarrow z=-3\]

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