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Math Help - Conic Sections

  1. #1
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    Conic Sections

    We are covering conic sections, including circles, parabolas, ellipses, and hyperbolas in pre-calculus. We were given a worksheet and there is one problem I just can't seem to grasp. here it is:

    Two suppliers, supplier 1 and supplier 2, are located at (0,0) and (6,0) respectively. They both charge $10 per mile (1 unit being a mile) for shipping their goods. In addition to the shipping cost, supplier 1 charges $980 for buying his goods and supplier 2 charges $1000 for his goods. Find a set of points (x,y) for which the total cost (shipping plus goods) is the same for both suppliers.
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  2. #2
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    You need to find the points of intersection of the two circles. The circle with center at (0,0) has radius r_1, the circle with center at (6,0) has radius r_2. Since supplier 1 charges $20 less than supplier 2, r_2 = r_1-2 describes the relationship between their radii such that the total cost is the same from each.

    The equations of the two circles are:
    x^2+y^2=r_1^2

    (x-6)^2+y^2=r_2^2=(r_1-2)^2

    Combine the two equations, and find the radical line to describe the set of points you're looking for.
    Circle-Circle Intersection -- from Wolfram MathWorld

    Some of the points you will find (if I did my math right):
    (4,0) at r_1=4
    \{(6,8), (6,-8)\} at r_1=10
    \{(20,48), (20,-48)\} at r_1=52
    \{(102,280), (102,-280)\} at r_1=298
    Last edited by Andre; January 14th 2010 at 10:45 PM.
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