Find an equation of the sphere with center at $(2, 1, −1)$ and radius $4$. Find an equation for the intersection of this sphere with the y-z plane; describe this intersection geometrically.
To solve this I used the following equation:
$(4)^2=(x-2)^2+(y-1)^2+(z+1)^2$
The equation for the intersection with the y-z plane happens when $x=0$ so the equation becomes $(4)^2=(y-1)^2+(z+1)^2$, which can be described geometrically this way:
$\{\left(2,y,z : y,z \in \mathbb R\right)\}$
Is this correct?