# find the center and radius

• Feb 27th 2007, 02:40 PM
rcmango
find the center and radius of the sphere: http://img175.imageshack.us/img175/3092/untitledxc6.png

• Feb 27th 2007, 02:54 PM
Jhevon
Quote:

Originally Posted by rcmango
find the center and radius of the sphere: http://img175.imageshack.us/img175/3092/untitledxc6.png

The equation of a sphere is in the form (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where the center is (h,k,l) and radius is r.

So our first objective is to get the equation in the form where we can just read of the center and the radius.

So here we go

x^2 + y^2 + z^2 - 2x - 4y + 6z - 2 = 0
=> (x^2 - 2x) + (y^2 - 4y) + (z^2 + 6z) = 2 ..........grouped like variables together. Now we will continue by completing the square for each section.

=> (x^2 - 2x + (-1)^2) + (y^2 - 4y + (-2)^2) + (z^2 + 6z + (3)^2) = 2 + (-1)^2 + (-2)^2 + 3^2
=> (x - 1)^2 + (y - 2)^2 + (z + 3)^2 = 16

Can you tell me the center and radius?
• Feb 27th 2007, 03:05 PM
Soroban
Hello, rcmango!

Quote:

Find the center and radius of the sphere: .x2 + y2 + z2 - 2x - 4y + 6z - 2 .= .0

We must "complete the square" . . .

. . (x² - 2x . . .) + (y² - 4y . . .) + (z² + 6z . . .) . = . 2

. . (x² - 2x + 1) + (y² - 4y + 4) + (z² + 6z + 9) . = . 2 + 1 + 4 + 9

. . . . . . . . . . . . . (x - 1)² + (y - 2)² + (z + 3)² . = . 16

Therefore: .C(1, 2, -3), .r = 4

Edit: Curses . . . too slow again!
• Feb 27th 2007, 03:12 PM
Jhevon
Quote:

Originally Posted by Soroban
Hello, rcmango!

We must "complete the square" . . .

. . (x² - 2x . . .) + (y² - 4y . . .) + (z² + 6z . . .) . = . 2

. . (x² - 2x + 1) + (y² - 4y + 4) + (z² + 6z + 9) . = . 2 + 1 + 4 + 9

. . . . . . . . . . . . . (x - 1)² + (y - 2)² + (z + 3)² . = . 16

Therefore: .C(1, 2, -3), .r = 4

Edit: Curses . . . too slow again!

Sorry Soroban. Topsquark beat me to a problem i was typing up earlier as well. I'll tell you what he told me, "it happens" :D However, what you did was not without waste, your formating and colors make the method easier to follow.
• Feb 27th 2007, 08:29 PM
rcmango
Thats alright! I examined both of your explanations and i understand it much better now. Thanks for all the help.