# Translate/shift ECEF coordinates given certain distance

I have some orbits in ECEF coordinates overlapped at the origin, and I would like to "move" some of them given a certain distance from the original orbit similar to the following picture:

But as you can see, the shift is not correctly done because the orbit sometimes "colides". For the shift I'm showing I used the following equations:

x_new = x_coord - distance*cos(inclination)
y_new = y_coord - distance*sin(inclination)


So my question is, how I can make this shift of a 3d coordinates giving a distance from original orbit/coordinate. What I'm missing for do it correctly? Thanks!