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

any help please.

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- Feb 27th 2007, 03:40 PMrcmangofind the center and radius
find the center and radius of the sphere: http://img175.imageshack.us/img175/3092/untitledxc6.png

any help please. - Feb 27th 2007, 03:54 PMJhevon

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, 04:05 PMSoroban
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, 04:12 PMJhevon
- Feb 27th 2007, 09:29 PMrcmango
Thats alright! I examined both of your explanations and i understand it much better now. Thanks for all the help.