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

  • question_answer
    The lengths of tangents from a fixed point to three circles of coaxial system are \[{{t}_{1}},{{t}_{2}},{{t}_{3}}\]and if P, Q and R be the centres, then \[QRt_{1}^{2}+RPt_{2}^{2}+PQt_{3}^{2}\]is equal to

    A)            1    

    B)            2

    C)            3    

    D)            0

    Correct Answer: D

    Solution :

               Co-axial system\[{{x}^{2}}+{{y}^{2}}+2gx+c=0\], (g variable)                    L.H.S. = \[\Sigma ({{g}_{2}}-{{g}_{3}})({{h}^{2}}+{{k}^{2}}-c+2{{g}_{1}}h)=0\]                    Since \[\Sigma ({{g}_{2}}-{{g}_{3}})=0\] and \[\Sigma {{g}_{1}}({{g}_{2}}-{{g}_{3}})=0\].


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