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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    Which of the following is a point on the common chord of the circle\[{{x}^{2}}+{{y}^{2}}+2x-3y+6=0\] and\[{{x}^{2}}+{{y}^{2}}+x-8y-13=0\]

    A)  (1, 4)                                    

    B)  (1, -2)

    C)  (1, -4)                                  

    D)  (1, 2)

    Correct Answer: C

    Solution :

    Let \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2x-3y+6=0\] \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+x-8y-13=0\] So, the common chord is given by                 \[{{S}_{1}}-{{S}_{2}}=0\] \[\therefore \] Common chord is \[({{x}^{2}}+{{y}^{2}}+2x-3y+6)\]                                                             \[-({{x}^{2}}+{{y}^{2}}+x-8y-13)=0\] \[2x-x-3y+8y+13+6=0\]                                 \[x+5y+19=0\] and this equation of common chord is satisfied by(1, -4) only


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