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In this paper, the kinematics of the tsunami wave ray and the wave front in the area, where the depth increases proportional to the squared distance to the straight shoreline, is studied. The exact analytical solution for the wave-ray trajectory above the parabolic bottom topography has been derived. This solution gives the possibility to determine in the ray approximation the tsunami wave heights in an area with the parabolic bottom topography. The distribution of the wave-height maxima in the area with such a bathymetry is compared to that obtained with a shallow-water model. All the exact solutions obtained can be used for testing numerical algorithms.