We report the discovery and confirmation of two new hot Jupiters discovered by the Transiting Exoplanet Survey Satellite (TESS): TOI 564 b and TOI 905 b. The transits of these two planets were initially observed by TESS with orbital periods of 1.651 d and 3.739 d, respectively. We conducted follow-up observations of each system from the ground, including photometry in multiple filters, speckle interferometry, and radial velocity measurements. For TOI 564 b, our global fitting revealed a classical hot Jupiter with a mass of $1.463^{+0.10}_{-0.096} M_J$ and a radius of $1.02^{+0.71}_{-0.29} R_J$. TOI 905 b is a classical hot Jupiter as well, with a mass of $0.667^{+0.042}_{-0.041} M_J$ and radius of $1.171^{+0.053}_{-0.051} R_J$. Both planets orbit Sun-like, moderately bright, mid-G dwarf stars with V ~ 11. While TOI 905 b fully transits its star, we found that TOI 564 b has a very high transit impact parameter of $0.994^{+0.083}_{-0.049}$, making it one of only ~20 known systems to exhibit a grazing transit and one of the brightest host stars among them. TOI 564 b is therefore one of the most attractive systems to search for additional non-transiting, smaller planets by exploiting the sensitivity of grazing transits to small changes in inclination and transit duration over the time scale of several years.
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