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The purpose of the paper is to analyze the Tzitzeica curve equation from the point of view of symmetry analysis theory. The Tzitzeica curve equation is a nonlinear ordinary differential equation that arises from differential geometry that may be regarded as a differential equation in three unknown functions, namely, the functions that give the parametrical representation of the curve. The extended classical symmetries, the generalized equivalence transformations and the equivalence transformations related to this nonlinear ordinary differential equation are determined.