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

  • question_answer
    Circle \[{{x}^{2}}+{{y}^{2}}-4x-8y-5=0\]will intersect the line \[3x-4y=m\] in two distinct points, if

    A)            \[-10<m<5\]                           

    B)            \[9<m<20\]

    C)            \[-35<m<15\]                         

    D)            None of these

    Correct Answer: C

    Solution :

               Radius of given circle > Perpendicular distance from the centre of circle to the given line.                    \[\Rightarrow \sqrt{4+16+5}>\frac{3(2)-4(4)-m}{\sqrt{9+16}}\]                    \[\Rightarrow \pm 25>-10-m\Rightarrow m+10>\pm 25\]\[\Rightarrow -35<m<15\].


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