In the unified definition of conic, the ratio of the distance from a fixed point to a fixed straight line is a constant e (e >; 0) is called a conic curve. This straight line is called a directrix. 0<e< is in 1, and the trajectory is elliptical; E= 1, and the trajectory is parabola; E> is in 1, and the trajectory is hyperbolic. Parabolic directrix is related to p value.

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.

Refer to Baidu Encyclopedia-Alignment