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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

  • question_answer
    A circle touches the line\[2x-y-1=0\]at point (3,5). Its centre lies on the line\[x+y=5,\]then the coordinates of centre of circle are

    A)  \[(-3,\text{ }8)\]            

    B)  (2, 3)

    C)  (3, 2)             

    D)  None of these

    Correct Answer: A

    Solution :

     Equation of line perpendicular to\[2x-y-1=0\]is \[x+2y+\lambda =0\] It passes through the point (3, 5) \[\therefore \] \[3+2\times 5+\lambda =0\] \[\Rightarrow \] \[\lambda =-13\] \[\therefore \] Equation is\[x+2y=13\]             ...(i) Centre of circle lies on the line\[x+y=5\]...(ii) On solving Eqs. (i) and (ii), we get \[x=-3,y=8\] Hence, coordinates of centre of circle is\[(-3,8)\]


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