The given equation of sphere is:
[tex] x^{2}+y^{2}+8x-6y+2z+17=0 [/tex]
Regrouping the variables together,
[tex] (x^{2}+8x)+(y^{2}-6y)+(z^{2}+2z)+17=0 [/tex]
We will use completing the square method, in this method we will consider the coefficients of x, y and z individually, then we will divide the coefficients by 2. Further, we will square the number obtained after dividing. At last we will add and subtract the number obtained.
[tex] (x^{2}+8x+16)-16+(y^{2}-6y+9)-9+(z^{2}+2z+1)-1+17=0 [/tex]
[tex] (x+4)^{2}+(y-3)^{2}+(z+1)^{2}=26-17 [/tex]
[tex] (x+4)^{2}+(y-3)^{2}+(z+1)^{2}=9 [/tex]
[tex] (x+4)^{2}+(y-3)^{2}+(z+1)^{2}=(3)^{2} [/tex]
is the standard form of the sphere with center [tex] (-4,3,-1) [/tex] and radius as 3.
