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Math Help - Sphere in the First Octant

  1. #1
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    Sphere in the First Octant

    Hi im having trouble with this problem.
    Find an equation of the largest sphere with the given center that is contained in the first octant. (6, 4, 9)

    So I thought that the radius would be distance from the center to the origin.
    I get 36+16+81=133 for my r squared

    so i submitted this equation and don't have it right. i feel like its something simple im missing
    (x-6)^2+(y-4)^2+(z-9)^2=133
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by fizzle45 View Post
    Hi im having trouble with this problem.
    Find an equation of the largest sphere with the given center that is contained in the first octant. (6, 4, 9)

    So I thought that the radius would be distance from the center to the origin.
    I get 36+16+81=133 for my r squared

    so i submitted this equation and don't have it right. i feel like its something simple im missing
    (x-6)^2+(y-4)^2+(z-9)^2=133
    The radius would have to be 4. Given the coordinates of the center, we know it can't be 9 units (otherwise it passes the xz and yz planes (going outside of the first octant), and it can't 6 units, since it will pass the xz plane.

    Thus, the only suitable radial value would be 4.

    Therefore, the equation of the sphere is (x-6)^2+(y-4)^2+(z-9)^2=16
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