Someone pointed in out in another thread of ours that it is only necessary to show that there is a single point of intersection to prove tangency. In this case, I think the easiest approach is to take 4y-3x=20 and isolate one of the variables. Next, substitute your result into the circle and find the single point of tangency.

Repeat the same process with 4y-3x=20 and the parabola.