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

  • question_answer
    The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}-{{y}^{2}}-8x+12=0\]is            [EAMCET  1990]

    A)            1    

    B)            2

    C)            3    

    D)            4

    Correct Answer: C

    Solution :

               Here\[{{C}_{1}}=(0,\ 0),\ {{r}_{1}}=2,\ {{C}_{2}}=(4,\ 0)\], \[{{r}_{2}}=2\]                    Here\[{{C}_{1}}{{C}_{2}}=4={{r}_{1}}+{{r}_{2}}\].                    Thus two circles touch externally, hence, the number of common tangents is 3.


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