Question

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

Answer 1

Answer:

(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)