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ChrisS

  • 4 years ago

Would someone mind checking this for me? Find the center and radius of the sphere given by the equation \[3x ^{2}+3y^{2}+3z^{2}+2y-2z=9\] \[x^{2}+y^{2}+\frac{2}{3}y+z^{2}-\frac{2}{3}z=3\ (regroup\ and\ divide\ by\ 3)\] \[x^{2}+y^{2}+\frac{2}{3}y+\frac{1}{9}+z^{2}-\frac{2}{3}z+\frac{1}{9}=3-\frac{1}{9}-\frac{1}{9}\ (Complete\ the\ \Square)\] \[x^{2}+(y+\frac{1}{3})^{2}+(z-\frac{1}{3})^{2}=\frac{25}{9}\] \[Center\ (0,-\frac{1}{3},\frac{1}{3}),\ radius\ \frac{5}{3}\]

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  1. amistre64
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=3x%5E2+%2B3y%5E2+%2B3z%5E2+%2B2y%E2%88%922z%3D9+

  2. amistre64
    • 4 years ago
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    centers good, radius seems off a bit

  3. dumbcow
    • 4 years ago
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    looks pretty good. the only thing i see is when you complete the square you should have added 2/9 to right side

  4. amistre64
    • 4 years ago
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    i tend to divide off the 3 after i complete the square parts to avoid fractions

  5. ChrisS
    • 4 years ago
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    right... I subtracted it instead of added... thanks!

  6. ChrisS
    • 4 years ago
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    so my radius should be \[\frac{\sqrt{29}}{3}\]

  7. amistre64
    • 4 years ago
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    yep

  8. ChrisS
    • 4 years ago
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    awesome. thanks to you both :)

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