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Math Help - Equation of a circle?

  1. #1
    Junior Member Kaloda's Avatar
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    Equation of a circle?

    Find the equation of the circle which is tangent to all four of the circles characterized by these four equations:

    x^2+y^2+10x=0
    x^2+y^2-10x=0
    x^2+y^2+10y=0
    x^2+y^2-10y=0

    ???
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  2. #2
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    If it's tangent to all four of the circles, then the derivatives will be equal at the points where they touch.
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  3. #3
    Senior Member abhishekkgp's Avatar
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    x^2+y^2=100 should be the required circle.
    this is because the radius of each circle is 5 units and their centres are at (-5,0), (5,0), (0,5) and (0,-5).
    if you draw a rough figure its easy to see that a symmetric flower shaped digram appears. and then its easy to find the required circle.
    In general a circle tangent to four given circles will not exist. In this special symmetric situation it exists.
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  4. #4
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    Quote Originally Posted by Kaloda View Post
    Find the equation of the circle which is tangent to all four of the circles characterized by these four equations:

    x^2+y^2+10x=0
    x^2+y^2-10x=0
    x^2+y^2+10y=0
    x^2+y^2-10y=0

    ???
    The graph of the 4 circles and the one tangent to them:
    Attached Thumbnails Attached Thumbnails Equation of a circle?-graph2.jpg  
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