Edit: Thanks to Christian Blatter I correct a misunderstanding in the "oblate ellipsoid" definition I previously used in this answer.
With "radius" we mean the distance between any given point on the Earth surface and the center of the Earth itself.
If we approximate the Earth to an oblate ellipsoid, then, cutting it by any plane parallel to the one containing the equatorial circle, we obtain a circle as section. This is because an oblate ellipsoid is obtained by revolution of a given ellipse along the minor axis. In the case of the Earth the minor axis lies on the pole-pole line.
The distance between a point on the section and the center of the section itself (i.e. the center of the circle) does not depends on the longitude of the point itself.
In other words, for points with the same latitude the radius does not depend on the longitude.
If we consider points with the same longitude, the radius depends on the latitude, instead. This is because the section obtained by considering any plane containing the the pole-pole axis is an ellipse. Moving along such ellipse the radius varies.
In summary, for points with the same longitude the radius depends on the latitude.