Set width of both parabola and catenary using one slider?

https://www.geogebra.org/m/kvtfc9zz

Just as a matter of mathematical tidiness, in the above, I can easily set the height and width of the parabola, but whereas 'height' works for both the parabola and the catenary, I have to use a separate slider 'fatness' to widen the the catenary. Would it be possible to have both curve's widths set using the same slider? IOW, can I 'solve for fatness'? To be clear, that means the same width where the curves cross the x axis.