find the center and radius of the sphere: http://img175.imageshack.us/img175/3092/untitledxc6.png
any help please.
find the center and radius of the sphere: http://img175.imageshack.us/img175/3092/untitledxc6.png
any help please.
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?
Hello, rcmango!
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!