A cycloid is a plane curve obtained as the locus of a point fixed on a circle, when the circle rolls on a straight line without slipping. Similar plane curves can be considered if we replace a base line with other curves such as parabola, hyperbola, circles. Conversely, we examine the inverse problem. That is, for a given curve, what is the base for which a fixed point on a rolling circle yields the curve as the locus? In general, this is hard to solve, but we discuss two approaches from viewpoints of differential equation and geometry. For the latter, we propose an implementation for the computational software Mathematica.