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In recent years, bistatic synthetic aperture radar (BiSAR) has attracted the attention of many radar researchers. It is well known that the slant range history of BiSAR is the sum of two square-rooted terms, which correspond to the transmitting and receiving slant ranges, respectively. For a point target in the SAR scene, it is quite difficult, if not impossible, to obtain an analytic formula to describe the target echo data in the 2-D frequency domain without any approximation by using the conventional stationary phase method, which makes it very difficult to develop fast-focusing algorithms for BiSAR. In this paper, based on the concept of an instantaneous Doppler wavenumber and by defining a new variable called half quasi-bistatic angle, an analytic formula of the point target response in the spectral domain is developed for BiSAR with parallel trajectory (referred to as parallel BiSAR for simplicity). Relying on a first-order Taylor expansion of the above formula with respect to the parameter called the sum of closest distances on the swath center, a bistatic range migration algorithm is proposed for any azimuth-shift-invariant BiSAR data processing. Simulation results have confirmed the effectiveness of the proposed novel approach.