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

  • question_answer
    The equation of a circle with centre \[(-4,\ 3)\] and touching the circle \[{{x}^{2}}+{{y}^{2}}=1\], is

    A)            \[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\]

    B)            \[{{x}^{2}}+{{y}^{2}}+8x+6y-11=0\]

    C)            \[{{x}^{2}}+{{y}^{2}}+8x+6y-9=0\]                            

    D)            None of these

    Correct Answer: A

    Solution :

               Centre is \[(-4,\ 3)\]                    Radius = Distance between centres ? Radius of other circle \[=5-1=4\]                    Hence equation of circle is \[{{x}^{2}}+{{y}^{2}}+8x-6y+9=0\].                    Trick: Only option (a) has centre (?4, 3).


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