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.

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