Show that the equation represent a sphere, and find its center and radius. X2+y2+z2+8x-6y-2z+17=0

(x - (-4)) ² + (y-3) ² + (z-1) ² = 3²

that is the equation for a sphere with radius 3 and center in (-4,3,1)

Step-by-step explanation:

from the equation

x²+y²+z²+8x-6y-2z+17=0

x²+y²+z²+8x-6y-2z+17 + (16-16+9-9+1-1) = 0

(x²+8x+16) + (y²-6y+9) + (z²-2z+1) + (17-16-9-1) = 0

(x+4) ² + (y-3) ² + (z-1) ² - 9 = 0

(x+4) ² + (y-3) ² + (z-1) ² = 9

(x - (-4)) ² + (y-3) ² + (z-1) ² = 3²

that is the equation for a sphere with radius 3 and center in (-4,3,1)