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BCECE Engineering BCECE Engineering Solved Paper-2013

  • question_answer
    If \[(-3,2)\] lies on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]which is concentric with the circle\[{{x}^{2}}+{{y}^{2}}+6x+8y-5=0,\] then C is equal to

    A)  11                         

    B)        \[-11\]                 

    C)  24                         

    D)         100

    Correct Answer: B

    Solution :

    Equation of family of concentric circles to the circle \[{{x}^{2}}+{{y}^{2}}+6x+8y-5=0\] \[{{x}^{2}}+{{y}^{2}}+6x+8y+\lambda =0\] which is similar to \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0.\] Thus, the point \[(-3,2)\] lies on the circle. \[{{x}^{2}}+{{y}^{2}}+6x+8y+c=0\] \[\Rightarrow \]\[{{(-3)}^{2}}+{{(2)}^{2}}+6(-3)+8(2)+c=0\] \[\Rightarrow \]\[9+4-18+16+c=0\] \[\therefore \]  \[c=-11\]


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