Abstract
This study deals with a special case in the geometry of 2D special plane curves. The research treaties the development of a method for locating points and drawing curves derived from moving points on two curved paths of conic sections, namely, circle and ellipse. The paper presents geometrical methods to determine points and nodes and to draw these melted-like curves in two cases. Parametric equations are also used to determine the ordinates of the points of each curve of the two cases of the curves. This research is the initial phase for the new type of curves and awaits future studies that will deal on 3D surfaces, such as a sphere, a right cone, or a right cylinder.
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