Field Programmable Gate Array (FPGA) based robust model fitting enjoys immense popularity in image processing because of its high efficiency. This paper focuses on the tradeoff analysis of real-time FPGA implementation of robust circle and ellipse estimations based on the random sample consensus (RANSAC) algorithm, which estimates parameters of a statistical model from a data set of feature points which contains outliers. In particular, this paper mainly highlights implementation alternatives for solvers of simultaneous equations and compares Gauss-Jordan elimination and Cramer's rule by changing matrix size and arithmetic processes. Experimental evaluation shows a Cramer's rule approach coupled with long integer arithmetic can reduce most hardware resources without unacceptable degradation of estimation accuracy compared to floating point versions.