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

  • question_answer
    If a line passing through origin touches the circle \[{{(x-4)}^{2}}+{{(y+5)}^{2}}=25\], then its slope should be

    A)            \[\pm \frac{3}{4}\]                  

    B)            0

    C)            \[\pm \,3\]                                 

    D)            \[\pm \,1\]

    Correct Answer: B

    Solution :

               Let equation of line be \[y=mx\] or \[y-mx=0\]                    Then applying condition for tangency,                    \[\left| \frac{-5-4m}{\sqrt{1+{{m}^{2}}}} \right|=5\Rightarrow 25+16{{m}^{2}}+40m=25+25{{m}^{2}}\]                    \[\Rightarrow 9{{m}^{2}}-40m=0\Rightarrow m=0\] or \[m=\frac{40}{9}\].


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