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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 the circles \[{{x}^{2}}+{{y}^{2}}-x=0,\,{{x}^{2}}+{{y}^{2}}+x=0\]is                         [EAMCET 1994]

    A)            2    

    B)            1

    C)            4    

    D)            3

    Correct Answer: D

    Solution :

               The centres and radii of the circles are                    Centres: \[{{C}_{1}}\left( \frac{1}{2},\ 0 \right)\,\,,\ {{C}_{2}}\left( -\frac{1}{2},\ 0 \right)\]                    Radii: \[{{r}_{1}}=\frac{1}{2},\ {{r}_{2}}=\frac{1}{2}\]                    Clearly, \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\]. Therefore the circles touch each other externally. Hence there are 3 common tangents.


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