Chapter 11 - Vectors and the Geometry of Space - 11.2 Exercises - Page 763: 41

$(x-1)^2+(y+3)^2+(z+4)^2=25$ Center: $(1,-3,-4)$ Radius: $5$

$x^2+y^2+z^2-2x+6y+8z+1=0$ $x^2+y^2+z^2-2x+6y+8z+1=(x-1)^2-1+(y+3)^2-9+(z+4)^2-16+1$ $=(x-1)^2+(y+3)^2+(z+4)^2-25=0$ $(x-1)^2+(y+3)^2+(z+4)^2=25$ Center: $(1,-3,-4)$ Radius: $5$