In this paper, one-parameter planar motion in the generalised complex plane
(or p-complex plane) ${C_p} = \left\{ {x + iy: x,y \in R, {i^2} = p} \right\}$
which is defined as a system of generalised complex numbers is studied.
Firstly, generalised Bobillier formula is obtained by using the geometric
interpretation of generalised Euler-Savary formula in the p-complex plane.
Moreover, it is shown
... [Show full abstract] that the Bobillier formula may be obtained by an
alternative method without the use of Euler-Savary formula in the generalised
complex plane. Thus, this formula generalises the complex, hyperbolic and
Galilean cases.