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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank System of circles

  • question_answer
    If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles\[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\] and \[{{x}^{2}}+{{y}^{2}}-4x+2y-44=0\] is 2 : 3, then the locus of P is a circle with centre [EAMCET 2003]

    A)            (7, - 8)                                      

    B)            (- 7, 8)

    C)            (7, 8)                                         

    D)            (- 7, - 8)

    Correct Answer: B

    Solution :

               \[\frac{{{x}^{2}}+{{y}^{2}}+2x-4y-20}{{{x}^{2}}+{{y}^{2}}-4x+2y-44}=\frac{2}{3}\]                      \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}+14x-16y+28=0\], \Centre =\[(-7,\,8)\].


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