Show that the equation represent a sphere, and find its center and radius. X2+y2+z2-6x+4y-2z=11

(x-3) ² + (y - (-2)) ² + (z-1) ² = 5²

that is the equation for a sphere with radius 5 and center in (3,-2,1)

Step-by-step explanation:

from the equation

x²+y²+z²-6x+4y-2z=11

x²+y²+z²-6x+4y-2z - 11 + (9-9+4-4+1-1) = 0

(x²-6x+9) + (y²+4y+4) + (z²-2z+1) + (-11-9-4-1) = 0

(x-3) ² + (y+2) ² + (z-1) ² - 25 = 0

(x-3) ² + (y+2) ² + (z-1) ² = 25

(x-3) ² + (y - (-2)) ² + (z-1) ² = 5²

that is the equation for a sphere with radius 5 and center in (3,-2,1)