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

  • question_answer
    Under what condition does the equation \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2uc+2uy+2wz+d=0\] represent a real sphere?

    A) \[{{u}^{2}}+{{v}^{2}}+{{w}^{2}}={{d}^{2}}\]

    B) \[{{u}^{2}}+{{v}^{2}}+{{w}^{2}}>d\]

    C) \[{{u}^{2}}+{{v}^{2}}+{{w}^{2}}<d\]

    D) \[{{u}^{2}}+{{v}^{2}}+{{w}^{2}}<{{d}^{2}}\]

    Correct Answer: B

    Solution :

    [b] Equation \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2ux+2vy+2wz+d=0\] Represent a real sphere if \[{{u}^{2}}+{{v}^{2}}+{{w}^{2}}>d\]


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