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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    The circles \[{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}-12y+27=0\] touch each other. The equation of their common tangent is  [MP PET 1998]

    A)            \[4y=9\]                                   

    B)            \[y=3\]

    C)            \[y=-3\]                                    

    D)            \[x=3\]

    Correct Answer: B

    Solution :

               \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}-12y+27=0\]                                      \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}-9=0\]                    The equation of common tangent is                    \[{{S}_{1}}-{{S}_{2}}=0\Rightarrow -12y+36=0\Rightarrow y=3\].


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