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

  • question_answer
     If the ratio of the lengths of tangents drawn from the point \[(f,g)\]to the given circle \[{{x}^{2}}+{{y}^{2}}=6\]and \[{{x}^{2}}+{{y}^{2}}+3x+3y=0\]be 2 : 1, then

    A)            \[{{f}^{2}}+{{g}^{2}}+2g+2f+2=0\]                            

    B)            \[{{f}^{2}}+{{g}^{2}}+4g+4f+4=0\]

    C)            \[{{f}^{2}}+{{g}^{2}}+4g+4f+2=0\]

    D)            None of these

    Correct Answer: C

    Solution :

               According to the condition, \[\frac{{{f}^{2}}+{{g}^{2}}-6}{{{f}^{2}}+{{g}^{2}}+3f+3g}=\frac{4}{1}\]\[\Rightarrow {{f}^{2}}+{{g}^{2}}+4f+4g+2=0\].


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