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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 normal to the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]parallel to the line \[x+2y=3\]is

    A)            \[2x+y-1=0\]                          

    B)            \[2x+y+1=0\]

    C)            \[x+2y-1=0\]                          

    D)            \[x+2y+1=0\]

    Correct Answer: C

    Solution :

               Any line parallel to \[x+2y=3\] is \[x+2y+\lambda =0\] and for this to be a normal to the given circle, must pass through its centre (1, 0), i.e. \[\lambda =-1\].                    So, normal is \[x+2y-1=0\].


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