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JEE Main & Advanced AIEEE Solved Paper-2007

  • question_answer
    Consider a family of circles which are passing through the point (-1, 1) and are touching X-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval       AIEEE  Solved  Paper-2007

    A)  \[4f\]                   

    B)  \[4f\]   

    C)         \[5f\]

    D)         \[5f\]

    Correct Answer: B

    Solution :

    Equation of circle which touches x-axis and coordinates of centre are (h, k), is \[{{(x-h)}^{2}}+{{(y-k)}^{2}}={{k}^{2}}\] \[\therefore \]It is passing through (-1, 1), then \[{{(-1-h)}^{2}}+{{(1-k)}^{2}}={{k}^{2}}\] \[\Rightarrow \]\[{{h}^{2}}+2h-2k+2=0\] \[\because \]For real circle, \[D\ge 0\]\[\Rightarrow \]\[2k-1\ge 0\] \[\Rightarrow \]\[k\ge \frac{1}{2}\]


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