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

  • question_answer
    Equation of radical axis of the circles \[{{x}^{2}}+{{y}^{2}}-3x-4y+5=0\], \[2{{x}^{2}}+2{{y}^{2}}-10x\]\[-12y+12=0\] is [RPET 2003]

    A)            \[2x+2y-1=0\]                        

    B)            \[2x+2y+1=0\]

    C)            \[x+y+7=0\]                           

    D)            \[x+y-7=0\]

    Correct Answer: A

    Solution :

               Circles are,                             \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}-3x-4y+5=0\]              ..... (i)                    and  \[{{S}_{2}}=2{{x}^{2}}+2{{y}^{2}}-10x-12y+12=0\]                    or   \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}-5x-6y+6=0\]              ..... (ii)                    \[\therefore \] Equation of radical axis is \[{{S}_{1}}-{{S}_{2}}=0\]                    \[\Rightarrow \] \[2x+2y-1=0\].


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