  We study within the linear response theory the far-infrared optical
absorption spectrum and the collective excitations of an asymmetric, wide
parabolic Al$_x$Ga$_{1-x}$As quantum well, consisting of two half-parabolas of
different curvatures, in the presence of an in-plane magnetic field. We employ
a self-consistent-field approach in the local-density approximation using
parameter values of a recent experimental study. At low $N_s$, there is only
one resonance corresponding to the lowest inter-Landau-level transition, and at
high $N_s$ we obtain two resonances at frequencies corresponding to the
different curvatures of the well, in good agreement with experiment. We also
calculate the optical spectra without any magnetic field and find similar
trends as a function of $N_s$, i.e., one resonance at low $N_s$ and two main
resonances at high $N_s$.}
