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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
    If the lines \[3x-4y+4=0\] and \[6x-8y-7=0\] are tangents to a circle, then the radius of the circle is  [IIT 1984; MP PET 1994, 2002; RPET 1995, 97; Kurukshetra CEE 1998]

    A)            3/2 

    B)            3/4

    C)            1/10                                          

    D)            1/20

    Correct Answer: B

    Solution :

               The diameter of the circle is perpendicular distance between the parallel lines (tangents) \[3x-4y+4=0\]and \[3x-4y-\frac{7}{2}=0\] and so it is equal to \[\frac{4}{\sqrt{9+16}}+\frac{7/2}{\sqrt{9+16}}=\frac{3}{2}\]. Hence radius is \[\frac{3}{4}\].


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