The results produced by the two formulas are very similar but not quite identical. But this length is that whole distance minus the focal length. If exact is not necessary the diagonal will do.
But how do I get the fractional error in focal length when neither D u nor D v are specified.
In the sign convention used in optical design a concave mirror has negative radius of curvature so. In order to be exact in solving for focal length you would need to know the aspect ratio of the sensor. By definition a 1 D lens focuses light at one meter. Note that the angle above A replaces this entire expression not just the a.