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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
    The centres of the circles \[{{x}^{2}}+{{y}^{2}}=1\], \[{{x}^{2}}+{{y}^{2}}+6x-2y=1\]  and \[{{x}^{2}}+{{y}^{2}}-12x+4y=1\] are  [MP PET 1986]

    A)            Same                                        

    B)            Collinear

    C)            Non-collinear                          

    D)            None of these

    Correct Answer: B

    Solution :

               Centres are (0, 0), (?3, 1) and (6, ?2) and a line passing through any two points say (0, 0) and (?3, 1) is \[y=-\frac{1}{3}x\] and point (6,?2) lies on it. Hence points are collinear.


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