This is the parabola with equation [math]y = x^2/4a[/math]. The parameter [math]a[/math] can be adjusted using the left hand slider.[br]By sliding the right-hand slider, you can roll the parabola along the x-axis.[br]The focus, [math]F[/math], is initially at [math](0,a)[/math]. What is the (cartesian equation of the) locus of [math]F[/math] as the parabola rolls?

Challenge: Can you reconstruct this GeoGebra applet yourself?