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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • question_answer
    If the circles \[{{x}^{2}}+{{y}^{2}}+5Kx+2y+K=0\]and \[2\left( {{x}^{2}}+{{y}^{2}} \right)+2Kx+3y1=0,(K\in R),\] intersect at the points P and Q, then the line \[4x+5yK=0\] passes through P and Q for : [JEE Main 10-4-2019 Morning]

    A) exactly two values of K

    B) exactly one value of K

    C) no value of K.

    D) infinitely many values of K

    Correct Answer: C

    Solution :

    Equation of common chord \[4kx+\frac{1}{2}y+k+\frac{1}{2}=0\]                              ....(1) and given line is \[4x+5yk=0\]          .....(2) On comparing (1) & (2), we get \[k=\frac{1}{10}=\frac{k+\frac{1}{2}}{-k}\]\[\Rightarrow \]No real value of k exist


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