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

  • question_answer
    The value of c,  for which the line \[y=2x+c\]is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}=16\], is [MP PET 2004; Karnataka CET 2005]

    A)            \[-16\sqrt{5}\]                          

    B)            20

    C)            \[4\sqrt{5}\]                             

    D)            \[16\sqrt{5}\]

    Correct Answer: C

    Solution :

               From\[c=\pm a\sqrt{1+{{m}^{2}}}\],                    Here, \[a=4,\,m=2\]                    \[\therefore \,c=\pm 4\sqrt{1+4}=\pm 4\sqrt{5}\].


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