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

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    Length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+5x+7y+9=0\]and \[{{x}^{2}}+{{y}^{2}}+7x+5y+9=0\]is  [Kurukshetra CEE 1996]

    A)            9    

    B)            8

    C)            7    

    D)            6

    Correct Answer: D

    Solution :

               Equation of common chord is \[{{S}_{1}}-{{S}_{2}}=0\]                    Þ \[2x-2y=0\] i.e., \[x-y=0\]                    \[\because \] Length of perpencicular drawn from \[{{C}_{1}}\] to \[x-y=0\] is \[\frac{1}{\sqrt{2}}\]                    \[\therefore \] Length of common chord \[=2\sqrt{\frac{19}{2}-\frac{1}{2}}=6\].


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