I use Autocad a lot, and a function I commonly use is offset, which takes a line and offsets it whatever distance you specify. An example would be that if you take a circle with a radius of $5$ ft and offset it $3$ ft, it gives you a new radius of $2$ ft. It also works with curves that are not circles -- it just takes every point on the line and shifts it a perpendicular distance of whatever you specify.
I was starting to wonder if it was possible to offset equations of a line in a similar way? Like an equation that was the exact same as $y = x^2$, but every point on it was a perpendicular distance of $5$ units, for example. I figured it would have to take on the form $y = ax^2 + 5$ (or $- 5$), but no idea how you would get that if it were even possible.