Step 1: The problem involves ellipses with the origin as the focus and \(x = 4\) as the directrix. For ellipses, the general property is that the sum of distances from any point on the ellipse to the two foci is constant.
Step 2: When we focus on the minor axis of an ellipse, the locus of the end of the minor axis behaves like a parabola. This is because the directrix and the focus define a parabolic shape, a known property of conic sections. The directrix acts as a line, and the focus remains fixed at the origin.
Step 3: Therefore, the locus of the end of the minor axis, given these conditions, forms a parabola.