I'd like to know what type of path the curved text commonly seen in logos takes. For example, consider the following logos (all pulled of a recent Google search):
Part of each logo is curved. In each case it appears that the curve is not along the path of a circle. It looks like it could be either a parabola or a hyperbolic sine, though I can't tell by eye. Presumably they used some graphic design software that rendered the image, so a correct answer can cite the practices of common software to achieve this effect.