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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 tangents to the circle \[{{x}^{2}}+{{y}^{2}}-22x-4y+25=0\] which are perpendicular to the line \[5x+12y+8=0\]are

    A)            \[12x-5y+8=0\], \[12x-5y=252\]

    B)            \[12x-5y=0,\,\,12x-5y=252\]

    C)            \[12x-5y-8=0,\,12x-5y+252=0\]

    D)            None of these

    Correct Answer: A

    Solution :

               Equation of line perpendicular to \[5x+12y+8=0\] is \[12x-5y+k=0\]. Now it is a tangent to the circle, if                    Radius of circle = Distance of line from centre of circle                    \[\sqrt{121+4-25}=\left| \frac{12(11)-5(2)+k}{\sqrt{144+25}} \right|\]\[\Rightarrow k=8\] or ? 252.                    Hence equations of tangents  are \[12x-5y+8=0\] and \[12x-5y=252\].


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