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

  • question_answer
    The equation of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\] which make equal intercepts on the positive coordinate axes is given by

    A)            \[x+y+2\sqrt{2}=0\]             

    B)            \[x+y=2\sqrt{2}\]

    C)            \[x+y=2\]                                

    D)            None of these

    Correct Answer: B

    Solution :

               Equation of tangent is of the form \[x+y+c=0\] and also it obeys condition of tangency, i.e., \[\left| \frac{-2+2+c}{\sqrt{2}} \right|=\sqrt{4+4-4}\Rightarrow c=\pm \,2\sqrt{2}\] But for positive intercepts, \[c=-2\sqrt{2}\] \ The tangent is \[x+y=2\sqrt{2}\].


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