Answer
Center: $(0,3,-4 )$ and radius: $5$
Work Step by Step
We know that the standard equation of a sphere is written as:
$(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=r^2\ \ \ $ (1)
Here, $(x_0,y_0,z_0)$ represents the center and $r$ is the radius of the sphere.
Since, we have $x^2+y^2+z^2-6y+8z=0$
or, $x^2+y^2-6y+z^2+8z=0$
or, $x^2+(y-3)^2+(z+4)^2=0+9+16$
or, $x^2+(y-3)^2+(z+4)^2=25$
or, $(x -0)^2+(y-3)^2+(z-(-4))^2=5$
Compare the above equation with equation (1), we get
Center: $(0,3,-4 )$ and radius: $5$
