Answer
Every normal line to the sphere passes through the center of the sphere.
Work Step by Step
Formula to calculate normal line equation is:
$\dfrac{(x_2-x_1)}{f_x(x_1,y_1,z_1)}=\dfrac{(y_2-y_1)}{f_y(x_1,y_1,z_1)}=\dfrac{(z_2-z_1)}{f_x(x_1,y_1,z_1)}$
At point$(p,q,r)$
$\dfrac{(x-p)}{2p}=\dfrac{(y-q)}{2q}=\dfrac{(z-r)}{2r}$
This implies:
$\dfrac{x}{p}=\dfrac{y}{q}=\dfrac{z}{r}$
Therefore, $x=y=z=0$
This means that:
Every normal line to the sphere passes through the center of the sphere.
