plotting – Labeling coordinate curves in ParametricPlot

I want to display a coordinate grid in parabolic coordinates:

ParametricPlot({-parabolic(r, phi), parabolic(r, phi)}, {r,0,1}, {phi,-1, 1},
  PlotStyle -> {Gray, Gray}, 
  BoundaryStyle -> Dashed, Mesh -> 9, Frame -> False, Ticks -> None)

Is there a relatively simply way to include labels for a selection of coordinate curves within the plot (essentially a ‘non-dynamic’ Tooltip)?