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Math Help - Calc 3 Problem - Don't understand

  1. #1
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    Unhappy Calc 3 Problem - Don't understand

    Find the equations of the two spheres that are tangent with equal radii whose centers are (-3,1,2) and (5,-3,6).

    I don't understand what it means when it says they are tangent with equal radii.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by tdat1979 View Post
    Find the equations of the two spheres that are tangent with equal radii whose centers are (-3,1,2) and (5,-3,6).

    I don't understand what it means when it says they are tangent with equal radii.
    First, find the distance between the two centers:

    D=\sqrt{(5-(-3))^2+(-3-1)^2+(6-2)^2}=\sqrt{64+16+16}=\sqrt{96}=4\sqrt{6}.

    If you take D and divide it by 2, you'll have two equal radii.

    Thus, the equation of the spheres are (x+3)^2+(y-1)^2+(z-2)^2=24 and (x-5)^2+(y+3)^2+(z-6)^2=24
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  3. #3
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    24?
    How did you get = 24? I don't understand where this number came from.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by inca2319 View Post
    24?
    How did you get = 24? I don't understand where this number came from.
    The distance between the two centers is 4\sqrt{6}. If they're to have the same radii, it would follow that r=\frac{4\sqrt{6}}{2}=2\sqrt{6}.

    Thus, r^2=2^2\cdot\sqrt{6}^2=4\cdot 6=24...
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  5. #5
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    Alright, I understand now. Thanks for the help!
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