## ChrisS 4 years ago Would someone mind checking this for me? Find the center and radius of the sphere given by the equation $3x ^{2}+3y^{2}+3z^{2}+2y-2z=9$ $x^{2}+y^{2}+\frac{2}{3}y+z^{2}-\frac{2}{3}z=3\ (regroup\ and\ divide\ by\ 3)$ $x^{2}+y^{2}+\frac{2}{3}y+\frac{1}{9}+z^{2}-\frac{2}{3}z+\frac{1}{9}=3-\frac{1}{9}-\frac{1}{9}\ (Complete\ the\ \Square)$ $x^{2}+(y+\frac{1}{3})^{2}+(z-\frac{1}{3})^{2}=\frac{25}{9}$ $Center\ (0,-\frac{1}{3},\frac{1}{3}),\ radius\ \frac{5}{3}$

1. amistre64
2. amistre64

centers good, radius seems off a bit

3. dumbcow

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

i tend to divide off the 3 after i complete the square parts to avoid fractions

5. ChrisS

6. ChrisS

so my radius should be $\frac{\sqrt{29}}{3}$

7. amistre64

yep

8. ChrisS

awesome. thanks to you both :)