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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 straight line \[4x+3y+\lambda =0\]touches the circle \[2({{x}^{2}}+{{y}^{2}})=5\], then \[\lambda \]is

    A)            \[\frac{5\sqrt{5}}{2}\]            

    B)            \[5\sqrt{2}\]

    C)            \[\frac{5\sqrt{5}}{4}\]            

    D)            \[\frac{5\sqrt{10}}{2}\]

    Correct Answer: D

    Solution :

               According to equation,                    \[\frac{4(0)+3(0)+\lambda }{\sqrt{{{4}^{2}}+{{3}^{2}}}}=\sqrt{\frac{5}{2}}\Rightarrow \lambda =\frac{5\sqrt{5}}{\sqrt{2}}=\frac{5\sqrt{10}}{2}\].


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