Question

find centre and radius of the sphere x^2+y^2+z^2+2x+4y+6z+5=0

Answer 1

The given equation can also be written as

(x^2+2x+1)+(y^2+4y+4)+(z^2+6z+9)+5-(14)=0.

(we have add 14 and subtract 14)

=>(x+1)^2+(y+2)^2+(z+3)^2=3^2

Hence, centre is (-1,-2,-3) and radius=3.

You can also find centre and radius by comparing the given equation with the standard equation of sphere.

I hope you will get it.