Answer:
Therefore, we conclude that the center of sphere at point
(27/3, -8/3, -8/3) with a radius 6.89.
Step-by-step explanation:
We have the formula for distance, we get
\sqrt{(x+3)^2+(y-4)^2+(z-4)^2} =2· \sqrt{(x-6)^2+(y-3)^2+(z+1)^2}
(x+3)^2+(y-4)^2+(z-4)^2=4·[(x-6)^2+(y-3)^2+(z+1)^2]
x²+6x+9+y²-8y+16+z²-8z+16=4x²-48x+4y²-24y+4z²+8z+184
3x²+3y²+3z²-54x+16y+16z=-143
(x²-54x/3)+(y²+16y/3)+(z²+16z/3)=-143/3
(x²-54x/3+729/9)+(y²+16y/3+64/9)+(z²+16z/3+64/9)=-143/3+729/9+2·64/9
(x-27/3)²+(y+8/3)²+(z+8/3)²=428/9
We calculate a radius \sqrt{428/9} =6.89
Therefore, we conclude that the center of sphere at point
(27/3, -8/3, -8/3) with a radius 6.89.
