ChrisS
  • ChrisS
Would someone mind checking this for me? Find the center and radius of the sphere given by the equation \[3x ^{2}+3y^{2}+3z^{2}+2y-2z=9\] \[x^{2}+y^{2}+\frac{2}{3}y+z^{2}-\frac{2}{3}z=3\ (regroup\ and\ divide\ by\ 3)\] \[x^{2}+y^{2}+\frac{2}{3}y+\frac{1}{9}+z^{2}-\frac{2}{3}z+\frac{1}{9}=3-\frac{1}{9}-\frac{1}{9}\ (Complete\ the\ \Square)\] \[x^{2}+(y+\frac{1}{3})^{2}+(z-\frac{1}{3})^{2}=\frac{25}{9}\] \[Center\ (0,-\frac{1}{3},\frac{1}{3}),\ radius\ \frac{5}{3}\]
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=3x%5E2+%2B3y%5E2+%2B3z%5E2+%2B2y%E2%88%922z%3D9+
amistre64
  • amistre64
centers good, radius seems off a bit
dumbcow
  • dumbcow
looks pretty good. the only thing i see is when you complete the square you should have added 2/9 to right side

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amistre64
  • amistre64
i tend to divide off the 3 after i complete the square parts to avoid fractions
ChrisS
  • ChrisS
right... I subtracted it instead of added... thanks!
ChrisS
  • ChrisS
so my radius should be \[\frac{\sqrt{29}}{3}\]
amistre64
  • amistre64
yep
ChrisS
  • ChrisS
awesome. thanks to you both :)

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