JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    The line \[y=x+c\]will intersect the circle \[{{x}^{2}}+{{y}^{2}}=1\]in two coincident points, if

    A)            \[c=\sqrt{2}\]                           

    B)            \[c=-\sqrt{2}\]

    C)            \[c=\pm \sqrt{2}\]                   

    D)            None of these

    Correct Answer: C

    Solution :

               \[y=x+c\] intersects at two coincident points, i.e. it is a tangent, therefore \[{{c}^{2}}=1(1+1)\Rightarrow c=\pm \sqrt{2}\].


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