Question

find the equation for the sphere and the radius. 2x^2 + 2y^2 + 2z^2 = 8x -24z +1. I keep getting r = 21/2 but the back of the book says r = 9/root 2

Answer 1

2x^2-8x+2y^2+2z^2+24z=1
x^2-4x+y^2+z^2+12z=1/2
(x-2)^2-4+y^2+(z+6)^2-36=1/2
(x-2)^2+y^2+(z+6)^2=(1/2)+4+36
(x-2)^2+y^2+(z+6)^2=81/2
(x-2)^2+y^2+(z+6)^2=(9/sqrt2)^2