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

  • question_answer
    Length of the tangent drawn from any point on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+{{c}_{1}}=0\] to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is [Kerala (Engg.) 2002]

    A)            \[\sqrt{{{c}_{1}}-c}\]             

    B)            \[\sqrt{c-{{c}_{1}}}\]

    C)            \[\sqrt{{{c}_{1}}+c}\]           

    D)            None of these

    Correct Answer: B

    Solution :

               Suppose \[({{x}_{1}},\ {{y}_{1}})\] be any point on first circle from which tangent is to be drawn, then                    \[x_{1}^{2}+y_{1}^{2}+2g{{x}_{1}}+2f{{y}_{1}}+{{c}_{1}}=0\]                    ?. (i)                    and also length of tangent                    \[=\sqrt{{{S}_{2}}}=\sqrt{x_{1}^{2}+y_{1}^{2}+2g{{x}_{1}}+2f{{y}_{1}}+c}\]      ?. (ii)                    From (i), we get (ii) as\[\sqrt{c-{{c}_{1}}}\].


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