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)

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

just needed some points but try socratic