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Simultaneous estimation of radial distortion, epipolar geometry, and relative camera pose can be formulated as a minimal problem and solved from a minimal number of image points. Finding the solution to this problem leads to solving a system of algebraic equations. In this paper, we provide two different solutions to the problem of estimating radial distortion and epipolar geometry from eight point correspondences in two images. Unlike previous algorithms which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We first simplify this system by eliminating six of these variables and then solve the system by two alternative techniques. The first one is based on the Gröbner basis method and the second one on the polynomial eigenvalue computation. We demonstrate that our solutions are efficient, robust, and practical by experiments on synthetic and real data.