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

  • question_answer
    The two circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6=0\]and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\]touch each other. The equation of their common tangent is [DCE 1999]

    A)            \[x=3\]                                      

    B)            \[y=6\]

    C)            \[7x-12y-21=0\]                     

    D)            \[7x+12y+21=0\]

    Correct Answer: A

    Solution :

               Let S1 º x2 + y2 ? 2x + 6y + 6 = 0                    and S2 º x2 + y2 ? 5x + 6y + 15 = 0,                    then common tangent is S1 ? S2 = 0                    Þ 3x = 9 Þ x = 3.


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