JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    The equations of the circles which touch both the axes and the line \[x=a\] are

    A)  \[{{x}^{2}}+{{y}^{2}}\pm ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

    B) \[{{x}^{2}}+{{y}^{2}}+ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

    C)  \[{{x}^{2}}+{{y}^{2}}-ax\pm ay+\frac{{{a}^{2}}}{4}=0\]

    D)  None of these

    Correct Answer: C

    Solution :

    \[\Rightarrow \] \[{{\left( x-\frac{a}{2} \right)}^{2}}+{{\left( y\pm \,\frac{a}{2} \right)}^{2}}={{\left( \frac{a}{2} \right)}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-ax\pm \,ay+\frac{{{a}^{2}}}{4}=0\]

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