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

  • question_answer
    The equations of the tangents drawn from the point (0, 1) to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y=0\]are               [Roorkee 1979]

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

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

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

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

    Correct Answer: A

    Solution :

               Required equations are given by \[S{{S}_{1}}={{T}^{2}}\]                    \[\Rightarrow ({{x}^{2}}+{{y}^{2}}-2x+4y)(1+4)={{\{y-1(x)+2(y+1)\}}^{2}}\]                    \[\Rightarrow 2{{x}^{2}}-2{{y}^{2}}-3x+4y+3xy-2=0\]                    \[\Rightarrow (2x-y+1)(x+2y-2)=0\].


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