Line at infinity of the plane of the conic also intersects the conic in two
points. We classify conics based on the type of this intersection:**Hyperbola **
is a conic that intersects the line at infinity at **two real and
different** points, i.e. the line at infinity is a secant of the
hyperbola.

Asymptots of the hyperbola are the tangent lines in these points
at infinity.
**Parabola **is a conic that intersects the line at infinity in**
one **point (two points that coincide), i.e. the line at infinity is a tangent
of parabola. This point at infinity lies on the parabola's axis.

**Ellipse** is a conics that intersects the line at infinity in**
two imaginary** points.**Circle** is an ellipse that
passes through a special pair of conjugate points of the line at infinity. These
points are called **absolute points** of the plane.

Move point X in the figure 6.

Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja - 3DGeomTeh - Developing project of the University of Zagreb