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Math Help - Simple Circle Question

  1. #1
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    Simple Circle Question

    There's a circle with the equation:

    x^2 + y^2-6x + 2y -15 = 0

    Another Circle has the Center (11,14) and radius 8. A Point Q lies on Circle 1 and a Point R lies on Circle 2. Find the shortest possible distance.

    My solution was to find the distance between the 2 circles and from there I determined that they intersected. So from there I came to the conclusion that the shorest distance was 0 and this siuation occurs when Q=R.

    Am I right?

    Thanks.
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  2. #2
    Member pflo's Avatar
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    Quote Originally Posted by StephenPoco View Post
    There's a circle with the equation:

    x^2 + y^2-6x + 2y -15 = 0

    Another Circle has the Center (11,14) and radius 8. A Point Q lies on Circle 1 and a Point R lies on Circle 2. Find the shortest possible distance.

    My solution was to find the distance between the 2 circles and from there I determined that they intersected. So from there I came to the conclusion that the shorest distance was 0 and this siuation occurs when Q=R.
    I assume you need to find the shortest possible distance between the Q and R? And I don't have any idea what methods you used to find the distance between the 2 circles, but these two don't intersect.

    The equation for the first circle should be converted to a useful form by completing the square:
    x^2-6x + y^2+2y = 15
    (x-3)^2-9   +   (y+1)^2-1  =  15
    (x-3)^2+(y+1)^2=25
    So this circle is centered at (3,-1) and has a radius of 5.

    Draw a line segment from the center of one circle to the center of another. The length of this segment is:
    d=\sqrt{(11-3)^2+(14+1)^2}\implies d=17

    The shortest distance between the circles is this distance minus the two radii, which is 4 units. So the minimum distance between P and Q is 4.
    Last edited by pflo; May 26th 2010 at 09:39 PM. Reason: typo fixed
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  3. #3
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    Thanks for that. I must have screwed something up. I did what you did, but I got the distance betten the 2 centers to be less than the sum of their radii. Dumb mistake on my part. Thanks though.

    I usually use:

     x^2+y^2+2gx+2fy+c=0

    And from that, the center would be (-g,-f) and the radius \sqrt{g^2+f^2-c}

    Then some where along the line of finding the distance I screwed up. Silly me.
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