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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Chord of contact of tangent, Pole and Polar

  • question_answer
    The equation of the common chord of the circles \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and \[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\] is

    A)            \[x-y=0\]                                  

    B)            \[x+y=0\]

    C)            \[x+y={{a}^{2}}+{{b}^{2}}\]                                          

    D)            \[x-y={{a}^{2}}-{{b}^{2}}\]

    Correct Answer: A

    Solution :

               We know that the equation of common chord is \[{{S}_{1}}-{{S}_{2}}=0\], where \[{{S}_{1}}\] and \[{{S}_{2}}\] are the equations of given circles, therefore                    \[{{(x-a)}^{2}}+{{(y-b)}^{2}}+{{c}^{2}}-{{(x-b)}^{2}}-{{(y-a)}^{2}}-{{c}^{2}}=0\]                    \[\Rightarrow 2bx-2ax+2ay-2by=0\]                    \[\Rightarrow 2(b-a)x-2(b-a)y=0\Rightarrow x-y=0\].


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