Question

Complete the square to write the equation of the sphere in standard form then find the center and radius
x^2 + y^2 + z^2 + 7x - 2y + 12z + 23 = 0

Answer 1

\[\left( x^2+7x+49/4 \right)+\left( y^2-2 y+1 \right)+\left( z^2+12z+36 \right)=-23+49/4+1+36\]
\[\left( x+\frac{ 7 }{ 2 } \right)^2+\left( y-1 \right)^2+\left( z+6 \right)^2=\frac{ 49 }{ 4 }+14=\frac{ 49+56 }{ 4 }=\frac{ 105 }{ 4 }\]
centre is ?
Radius=?