Considering a complex optical system with several lens elements moving independently one from another, there is no direct relation between minimum focusing distance, maximum magnification and focal length. Other parameters have to be considered.
Anyway, most people speaking of variation in the angle of view, and not in focal length, when they talk about focus breathing, one can simplify things and consider each of the two lenses as if it were made of one single lens element. In this case, there is a direct relation between minimum focusing distance (MFD), maximum magnification (MM) and focal length at minimum focusing fistance (FL@MFD):
FL@MFD = MFD x MM.
HD Pentax-D FA 70-210 mm f/4 ED SDM WR: MFD = 0.95m MM = 0.32x ==> FL@MFD = 304mm. The angle of view decreases with the focusing distance.
HD Pentax-D FA★ 70-200mm f/2.8 ED DC AW: MFD = 1.2m MM = 0.13x ==> FL@MFD = 156mm. The angle of view increases when the focusing distance decreases.
Anyway, most people speaking of variation in the angle of view, and not in focal length, when they talk about focus breathing, one can simplify things and consider each of the two lenses as if it were made of one single lens element. In this case, there is a direct relation between minimum focusing distance (MFD), maximum magnification (MM) and focal length at minimum focusing fistance (FL@MFD):
FL@MFD = MFD x MM.
HD Pentax-D FA 70-210 mm f/4 ED SDM WR: MFD = 0.95m MM = 0.32x ==> FL@MFD = 304mm. The angle of view decreases with the focusing distance.
HD Pentax-D FA★ 70-200mm f/2.8 ED DC AW: MFD = 1.2m MM = 0.13x ==> FL@MFD = 156mm. The angle of view increases when the focusing distance decreases.