Question

Find the centre and the radius of the following sphere 2x²+2y²+2z²-2x+4y-6z=1.
Solution:
x²+y²+z²-x+2y-3z=1
x²+y²+z²+2ux+2vy+2wz+d=0
Centre=(-u,-v,-w)
=(1/2,1,3/2)
Radius r = (u²+v²+w²-d)½
=((-1/2)²+1²+(-3/2)-(-1/2))½
=(1/4+1+9/4+1/2)½
=(4)½
=2.​

Answer 1

Answer:

(1/2,,1,3/2). and radius=2