Rolling a parabola

Topic:
Parabola
This is the parabola with equation . The parameter can be adjusted using the left hand slider. By sliding the right-hand slider, you can roll the parabola along the x-axis. The focus, , is initially at . What is the (cartesian equation of the) locus of as the parabola rolls?
Challenge: Can you reconstruct this GeoGebra applet yourself?