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

  • question_answer
    If \[2x-4y=9\]and \[6x-12y+7=0\]are the tangents of same circle, then its radius will be                                           [Roorkee 1995]

    A)            \[\frac{\sqrt{3}}{5}\]              

    B)            \[\frac{17}{6\sqrt{5}}\]

    C)            \[\frac{2\sqrt{5}}{3}\]            

    D)            \[\frac{17}{3\sqrt{5}}\]

    Correct Answer: B

    Solution :

               Since the tangents are parallel, therefore the distance between these two tangents will be its diameter i.e., diameter \[=\frac{34}{\sqrt{180}}=\frac{17}{3\sqrt{5}}\]                    Hence, radius\[=\frac{17}{6\sqrt{5}}\].


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