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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank System of circles

  • question_answer
    The two circles \[{{x}^{2}}+{{y}^{2}}-4y=0\]and \[{{x}^{2}}+{{y}^{2}}-8y=0\] [BIT Ranchi 1985]

    A)            Touch each other internally   

    B)            Touch each other externally

    C)            Do not touch each other        

    D)            None of these

    Correct Answer: A

    Solution :

               \[{{r}_{1}}=2\]; \[{{r}_{2}}=4\]                    \[{{C}_{1}}{{C}_{2}}=2\]                    \[\because \ {{r}_{2}}-{{r}_{1}}={{C}_{1}}{{C}_{2}}\]                    \[\therefore \]Circle touches internally.


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