Please help me solve the following problem. Find the center and radius of the sphere, given the following equation. (Click to see)

Question

Please help me solve the following problem.  Find the center and radius of the sphere, given the following equation.  (Click to see)

babyslapmafro · Answer

$$2x^2-2x+2y^2-3y+2z^2+5z=2$$

babyslapmafro · Answer

I've solved problems like this before but I do not know what to do when there is a coefficient greater than one in front of the squared variable...

anonymous · Answer

dividing everything by two might make it easier to look at. but you're basically just completing the square for ever variable.

you're also allowed to do, for 2x^2 - 2x:

$$= (\sqrt{2}x - \frac{ 1 }{ \sqrt{2} })^2 - \frac{ 1 }{ 2 }$$

anonymous · Answer

so the answer is pi :D

anonymous · Answer

let me know if you have questions.

and for the location of the center, it's the same concept as 2d.

for (x - h)^2, h is the center's x-component because x = h makes (x - h)^2 = 0

so our x component is when x = 1/2