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We present refined parameters for the extrasolar planetary system HAT-P-2 (also known as HD 147506), based on new radial velocity and photometric data. HAT-P-2b is a transiting extrasolar planet that exhibits an eccentric orbit. We present a detailed analysis of the planetary and stellar parameters, yielding consistent results for the mass and radius of the star, better constraints on the orbital eccentricity and refined planetary parameters. The improved parameters for the host star are M★= 1.36 ± 0.04 M⊙ and R★= 1.64 ± 0.08 R⊙, while the planet has a mass of Mp= 9.09 ± 0.24 MJup and radius of Rp= 1.16 ± 0.08 RJup. The refined transit epoch and period for the planet are E= 245 4387.49375 ± 0.00074 (BJD) and P= 5.6334729 ± 0.0000061 (d), and the orbital eccentricity and argument of periastron are e= 0.5171 ± 0.0033 and forumla⁠. These orbital elements allow us to predict the timings of secondary eclipses with a reasonable accuracy of ∼15 min. We also discuss the effects of this significant eccentricity including the characterization of the asymmetry in the transit light curve. Simple formulae are presented for the above, and these, in turn, can be used to constrain the orbital eccentricity using purely photometric data. These will be particularly useful for very high precision, space-borne observations of transiting planets.