The aim of this article is the application of the parametric equations of the plane for the description of plane curves inud space R³. It is found a simple way of parameterization of the plane, which allows you to enter a local coordinateud system on the plane in space R³. In this local coordinate system of equations of plane curves look easy. In the paperud we consider the parameterization of the plane lines on the example of second-order curves. This view may be usefulud for analytical geometry and mechanics.
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