CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    If (2, 3, 5) is one end of a diameter of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2z+20=0,\]then co-ordinates of the other end of the diameter are:

    A)  (4, 3, 5)               

    B)        \[(4,9,-3)\]

    C)  (4, 9, 3)               

    D)        \[(4,3,-3)\]

    E)  (4, 9, 5)

    Correct Answer: B

    Solution :

    Let\[({{x}_{2}},{{y}_{2}},{{z}_{2}})\]be the co-ordinate of another end of diameter of sphere. Also centre of sphere is (3, 6, 1). \[\therefore \]  \[\frac{2+{{x}_{2}}}{2}=3\] \[\Rightarrow \]               \[{{x}_{2}}=4\]                 \[\frac{3+{{y}_{2}}}{2}=6\] \[\Rightarrow \]                               \[{{y}_{2}}=9\] and                        \[\frac{5+{{z}_{2}}}{2}=1\]           \[\Rightarrow \]                               \[{{z}_{2}}=-3\] \[\therefore \]Required point is\[(4,9,-3)\].


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