In the general theory of spatial surfaces, surfaces can be regarded as trajectories formed by a family of curves moving along their directrix. For a surface generated by a curve family, the directrix is a spatial curve that intersects every curve in the curve family.
Extended data:
Geometric properties of directrix;
The distance from the directrix to the vertex is Rn/e, and the distance from the directrix to the focus is p = rn (1+e)/e = l0/e.
When the eccentricity e is greater than zero, p is finite, and the distance from the directrix to the focus is p = rn (1+e)/e = l0/e.
When eccentricity e is equal to zero, P is infinite and P is irregular. It is unreasonable to define a conic with infinity.
The reason why limit is defined in textbooks is because we don't know the geometric properties of directrix. When e is equal to zero, the directrix is infinite, and the directrix is an abnormal quantity and a limit quantity. In textbooks, directrix is used to define why conic curves do not contain circles.
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