Answer
$y^2+z^2 =4x^2$ ; Circular cone.
Work Step by Step
The set of points for which the distance to the x-axis is twice the distance to the y-axis are the lines $y=2x$ and $y=-2x$
The traces parallel to the yz -plane will be circles.
$y^2=4x^2$
and $y^2+z^2 =4x^2$
So, we find that the rotated surface is a circular cone.