This work concerns mathematical analysis of equations describing turbulence in a quasi-geostrophic approximation, that is, a flow of large synoptic-scale structures in mid-lattitudes. Based on an analysis of numerical data it is expected that these equations may have very interesting mathematical properties [see Bernard et al, PRL 98, 024501 (2007)] - certain statistics may be invariant under the conformal transformations, that is, the transformations which can rescale lengths but preserve angles. The aim of this work is to perform the Lie group analysis of equations in the quasi-geostrophic approximation and to find, analytically, such transformations of variables which keep the equation unchanged.