  In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane $\mathbb{E}^2$ were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale $h$ identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system.
