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

  • question_answer
    If the line \[3x-4y=\lambda \]touches the circle \[{{x}^{2}}+{{y}^{2}}-4x-8y-5=0\], then \[\lambda \]is equal to [Roorkee 1972; Kurukshetra CEE 1996]

    A)            - 35, -15                                   

    B)            - 35, 15

    C)            35, 15                                       

    D)            35, -15

    Correct Answer: B

    Solution :

               Accordingly, \[\frac{3(2)-4(4)-\lambda }{\sqrt{{{3}^{2}}+{{4}^{2}}}}=\pm \sqrt{{{2}^{2}}+{{4}^{2}}+5}\]                    \[\Rightarrow -10-\lambda =\pm 25\Rightarrow \lambda =-35,\ 15\].


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