1. When the plane is parallel to the generatrix of the conic surface and does not pass through the vertex of the conic curve, the result is a parabola.

2. When the plane is parallel to the generatrix of the quadric surface and passes through the vertex of the quadric surface, the result degenerates into a straight line.

3. When the plane only intersects one side of the conic surface and does not pass through the vertex of the conic surface, the result is an ellipse.

4. When the plane intersects only one side of the conical surface, but not the vertex of the cone, and is perpendicular to the symmetry axis of the cone, the result is a circle. The median vertical line of the line segment between the moving point on the alignment and a point outside the line, and the trajectory of the intersection of the straight line perpendicular to the moving point and the alignment is a parabola.

5. When the plane intersects the two sides of the quadric surface and does not pass through the vertex of the quadric surface, the result is a hyperbola (each branch is the intersection of a quadric surface in this quadric surface and the plane).

The (incomplete) unified definition of conic: the locus of a point whose ratio of the distance r from a point to a point on a plane to the distance d from a point to a straight line is constant e=r/d is called conic. When e> 1 is hyperbola, when e= 1 is parabola, when 0

The fixed point is called the focus of the conic, the fixed line is called the directrix, and e is called the eccentricity. A cone is a geometric figure with two definitions. Analytic geometry definition: A spatial geometry consisting of a conical surface and a plane intersecting it (satisfying that the intersection line is a circle) is called a cone.