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JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer
    If P and Q are the points of intersection of the circles\[{{x}^{2}}+{{y}^{2}}+3x+7y+2p5=0\]and \[{{x}^{2}}+{{y}^{2}}+2x+2y{{p}^{2}}=0,\]then there is a circle passing through P, Q and (1, 1) for     AIEEE  Solved  Paper-2009 

    A) all values of p

    B) all except one value of p

    C) all except two values of p

    D) exactly one value of p

    Correct Answer: B

    Solution :

    Radical axis is \[x+5y+{{p}^{2}}+2p5=0\] Equation of circle is \[{{x}^{2}}+{{y}^{2}}+3x+7y+2p5+\lambda [x+5y+{{p}^{2}}+2p\] \[-5]=0\]                              ?. (i) (i) passes through (1, 1) \[\Rightarrow \]\[\lambda =\frac{-(2p+7)}{{{(p+1)}^{2}}}\]                          \[(p\ne -1)\]


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