in this context, formula_9 and formula_10 are called "hyperparameters" (parameters of the prior), to distinguish them from parameters of the underlying model (here "q"). it is a typical characteristic of conjugate priors that the dimensionality of the hyperparameters is one greater than that of the parameters of the original distribution. if all parameters are scalar values, then this means that there will be one more hyperparameter than parameter; but this also applies to vector-valued and matrix-valued parameters. (see the general article on the exponential family, and consider also the wishart distribution, conjugate prior of the covariance matrix of a multivariate normal distribution, for an example where a large dimensionality is involved.)