Answer
$-4x =y^2+z^2$ ; paraboloid.
Work Step by Step
A parabola has the equation $x=ay^2$ and the vertex of the parabola is the mid-point between the focus and directrix, which is $(0,0)$.
Let us consider that the distance from the vertex to the focus or directrix is $c=1$ and $a=\dfrac{1}{4c}=\dfrac{1}{4}$
Since the parabola opens in the right, we have
$x=\dfrac{-1}{4} y^2$
when $x=k$, then the traces are parallel to the yz plane.
Therefore, $x=\dfrac{-1}{4} y^2-\dfrac{1}{4} z^2 \implies -4x =y^2+z^2$
So, we find that the rotated surface is a paraboloid.
